What Is the Monte Carlo Analysis for Retirement?

If you are in retirement or planning on retiring soon, one of the most important questions you'll have is how much money is “enough.” You don't want to work longer than you need to, but you absolutely don't want to run out of money in retirement. There are many different ways to calculate how much money you can withdraw in retirement. A Monte Carlo analysis is one way to calculate how likely it is that you will have enough money for retirement.

What Is a Monte Carlo Simulation?

The concept of a Monte Carlo simulation was invented by John von Neumann and Stanislaw Ulam in the 1940s. They named it after the Monte Carlo casino in Monaco because a Monte Carlo simulation shares a lot of similarities with a roulette game.

In a Monte Carlo simulation, rather than use an average rate of return or something similarly deterministic, you define the list of possible inputs, randomly generate values based on the likely values for each input, and then deterministically calculate your desired output. After running hundreds or thousands of simulations, you can plot the results. Usually, they appear in a bell curve with the most likely outcomes being in the middle and outcomes that are less likely appearing on either end of the curve.

How Does Monte Carlo Relate to the 4% Rule?

Monte Carlo simulations are popular in a number of different fields, including biology, statistics, physics, chemistry, cryptography, artificial intelligence, and finance. One popular usage for Monte Carlo simulations is in retirement planning, specifically in helping people calculate whether they have saved enough money to retire.

The 4% rule is a simple method that people sometimes use to determine how much money they need to retire. The 4% rule for safe withdrawals says that you can safely withdraw and live off of 4% of your principal each year. If you need $40,000 annually, you can safely retire once you have $1 million. Critics of the 4% rule say that it is overly simplistic and doesn't account for many of the different variables that affect retirement planning.

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The Risk of Retirement

Should You Run Monte Carlo Simulations as You Plan for Retirement?

We have written before about some of the limitations of choosing a single “safe withdrawal” number. Running Monte Carlo simulations for retirement planning can be one way to more accurately portray the range of possible outcomes.

To run a Monte Carlo retirement simulation, first choose the possible variables, which might include (among other possibilities):

• How long you're likely to live
• Your asset allocation, and the expected annual return for each asset class
• Inflation rates
• Tax rates
• Annual withdrawal amount

For each of these initial variables, you randomly select a value from among the most likely outcomes. For example, if you have a mean life expectancy of 77 with a likely standard deviation of 10 years either way, you pick a random number between 67 to 87 (with numbers closer to the mean being more likely). Once you select values for each of the initial inputs, you can run a deterministic calculation to determine if you'll run out of money before you die or, if not, how much money you'll have when you pass away.

Running this simulation hundreds or thousands of times (with different random initial inputs) will give you a plot of the expected outcomes. That can give you an idea of how likely different outcomes are. You may be comfortable with a 1% likelihood of running out of money before you die but maybe not with a 10% chance.

While you don't have to run a Monte Carlo simulation as you plan for retirement, it can give you another data point for how likely you are to have enough money to last for the rest of your life.

How Does the Sequence of Return Risks Affect Monte Carlo Simulations?

One of the biggest risks in retiring is called a “sequence of return risk.” The sequence of return risk refers to the fact that the order in which you get various returns is important. If you have money invested in an asset that is expected to give an 8% annual return, that doesn't mean that it will earn 8% every year. Instead, it might be up 25% in some years and down 10% in other years. The 8% figure refers to the fact that over a long period of time, the expected annual rate of return is 8% (and of course, that return is not guaranteed).

It turns out that the order these returns come in is crucial to retirement planning. If you retire right when the stock market or economy suffers a sustained downturn, that can devastate your finances and drastically increase the chances that your money will not last (you'd basically be selling low without a chance for you to refill your retirement coffers). Running a Monte Carlo simulation can help you identify how likely you are to fall victim to the sequence of return risk.

More information here:

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A Framework for Thinking About Retirement Income

The Bottom Line

A Monte Carlo analysis is a tool that is used in a variety of scientific and sociological fields. One of the most popular ways people use a Monte Carlo analysis is for retirement planning. To run a Monte Carlo simulation, you first identify your initial inputs. The simulation then chooses a random value based on the likely possibilities. Running the simulation thousands of times can help you visualize the likely outcomes for your retirement planning and identify how likely you are to experience the sequence of return risk.

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