# Planning Retirement Using the Monte Carlo Simulation

How this method can improve retirement projections

There is no foolproof way to predict the future, but a Monte Carlo simulation that allows for the real possibility of disaster can give a clearer picture of how much money to safely withdraw from retirement savings.

Here's how the Monte Carlo method works and how to apply it to retirement planning. It's also important to understand where it can fall short and how to correct for that.

### Key Takeaways

• A Monte Carlo simulation can be used to test if one will have enough income throughout retirement.
• Unlike a traditional retirement calculator, the Monte Carlo method incorporates many variables to test possible retirement portfolio outcomes.
• Critics claim this method can underestimate major market crashes, but there are ways to compensate.

## Understanding the Monte Carlo Simulation

The Monte Carlo simulation is a mathematical model used for risk assessment named after Monaco's gambling mecca. People who are trying to plan for a secure retirement and can't afford to lose their savings don't want to take chances with their money. So why turn to a Monte Carlo simulation for guidance?

Although this name for the calculation may seem ironic, it is a planning technique used to calculate the percentage probability of specific scenarios based on set assumptions and standard deviations. The Monte Carlo method has often been used in investment and retirement planning to project the likelihood of achieving financial or retirement goals, and whether a retiree will have enough income given a wide range of possible outcomes in the markets.

There are no absolute parameters for this type of projection. Underlying assumptions for these calculations typically include such factors as interest rates, the client's age and the projected time to retirement, the amount of the investment portfolio spent or withdrawn each year, and the portfolio allocation. The computer model then runs hundreds or thousands of possible outcomes using historical financial data.

The results of this analysis usually come in the form of a bell curve. The middle of the curve delineates the scenarios that are statistically and historically the most likely to happen. The ends—or tails—measure the diminishing likelihood of the more extreme scenarios that could occur.﻿﻿

Scenarios via Monte Carlo simulations can give a clearer picture of risk, such as whether a retiree will outlive retirement savings.

## Limitations to Consider

Market turbulence has exposed a weakness that seems to afflict this method.

Supporters point out that Monte Carlo simulations generally provide much more realistic scenarios than simple projections that assume a given rate of return on capital. Critics contend that Monte Carlo analysis cannot accurately factor infrequent but radical events, such as market crashes, into its probability analysis. Many investors and professionals who used this method were not shown a real possibility of such market performance as a financial crisis, according to research.

In his paper "The Retirement Calculator from Hell," William Bernstein illustrates this shortcoming.﻿﻿ He uses an example of a series of coin tosses to prove his point, where heads equals a market gain of 30% and tails a loss of 10%.

• Starting with a \$1 million portfolio and tossing the coin once a year for 30 years, a saver will end up with an average annual total return of 8.17%. That means that they could withdraw \$81,700 per year for 30 years before exhausting the principal.
• A saver who flips tails every year for the first 15 years, however, would only be able to withdraw \$18,600 per year. A saver lucky enough to flip heads the first 15 times could annually take out \$248,600.

And while the odds of flipping either heads or tails 15 times in a row seems statistically remote, Bernstein further proves his point using a hypothetical illustration based on a \$1 million portfolio that was invested in five different combinations of large- and small-cap stocks and five-year Treasuries in 1966. That year marked the beginning of a 17-year stretch of zero market gains when one factors in inflation.

History shows that the money would have been exhausted in less than 15 years at the mathematically-based average withdrawal rate of \$81,700. In fact, withdrawals had to be cut in half before the money lasted the full 30 years.

## How to Plan Realistically

There are a few basic adjustments that experts suggest to help remedy the shortcomings of Monte Carlo projections. The first is to simply add on a flat increase to the possibility of financial failure that the numbers show, such as 10% or 20%.

Another is to plot out projections that use a percentage of assets each year instead of a set dollar amount, which will greatly reduce the possibility of running out of principal.

## The Bottom Line

﻿The Monte Carlo simulation can be used to help plan for retirement. It predicts different outcomes that will affect how much it is safe to withdraw from retirement savings over a given period of time. Critics contend that it can underestimate major bear markets. Experts, however, suggest a few ways to overcome the shortcomings of the model.

Article Sources
Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
1. LibreTexts Statistics Library. "The Monte Carlo Simulation Method."

2. William J. Bernstein. "The Retirement Calculator from Hell."

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