**Monte Carlo Analysis in Retirement Planning: Will I Run Out of Money?**

Barbara O’Neill, Ph.D., CFP®, Rutgers Cooperative Extension, oneill@aesop.rutgers.edu

“Monte Carlo analysis.” The words make you think of a European gambling mecca, don’t they? It fact, where retirement planning is concerned, Monte Carlo analysis is actually somewhat related to gambling. It is a technique used to reduce the gamble that many people take when they decide to retire and live off of their savings. In other words, Monte Carlo analyses (also refereed to as simulations) help answer the following question: will you outlive your retirement assets or will you have enough money saved to last you well into your late 80s or 90s?

Below is a brief explanation of Monte Carlo analysis. To understand it better, however, it is helpful to compare Monte Carlo analysis to other types of retirement planning tools. Many simple retirement calculations produce projections of required retirement savings using fixed average annual rates of return (e.g., 7% or 8%) on investments. These fixed figures are generally based upon an expected investment strategy (e.g., how much stock is held in an investor’s portfolio) and historical rates of return.

From 1926-2011, large company U.S. stocks had a 9.8% average annual return, compared to 5.7% for long-term government bonds and 3.6% for Treasury bills, according to Chicago investment research firm Ibbotson Associates. Historically, the more stock investors hold in their portfolio, the higher the average annual return over the long term.

While better than doing no calculation at all, fixed rate planning tools have one major flaw. History also tells us that there is not a diversified portfolio that will reliably produce the expected average return annually or even after decades have passed. Instead, investment returns, especially for stocks, are usually all over the map and can go through prolonged slumps that can last years such as 2000-2002 and 2007-2009.

If you count on an average annual return of 10% over 30 years, and spend according to this expectation, but instead average a return of 7%, you might be living a severely reduced lifestyle by the time you are 80. Of course, to be fair, there is also the probability that you will earn a higher return than planned and become a multimillionaire. But this “upside risk” is not the one most people are worried about. Rather, they are concerned about the chance of outliving their money.

So how does Monte Carlo analysis help? By inserting additional criteria into a retirement planning calculation. Many financial planners use 30-year standard deviations to test the expected rate of return on retirement projections. Standard Deviation is a measure of volatility (e.g., highs and lows) of investment returns. Financial advisors often use specialized software to randomly change the rate of return to cover a wide range of possible outcomes. With each change, the software records how much money a person is left with at the end of their life.

After a Monte Carlo analysis is complete, a financial planner can show what percent of the time a client still had money left over after a long period of time. He or she then seeks to craft a plan that provides both an acceptable spending level for the person and an acceptable probability that assets won’t be depleted. Often, key variables in the simulation (e.g., age at retirement and amount of money needed) are adjusted to find an outcome that works. The term “safe withdrawal” refers to the amount that retirees can withdraw from retirement savings without running out of money during a specified period of time (e.g., 30 years).

Key factors in determining a safe withdrawal rate include: the amount of accumulated savings, the number of years that assets are desired to last, expected income from Social Security and a pension, a person’s expected retirement age, and the asset allocation (i.e., percentage of savings in stocks, bonds, real estate, and cash assets) of a retiree’s investment portfolio. Several factors are, of course, unknown and must be assumed, such as a person’s actual life expectancy and actual return on investments.

Of course, it is up to investors and/or their financial advisors to make necessary portfolio asset allocation adjustments to match their desired simulation outcome. They must also monitor and revise retirement plans as necessary to ensure no unpleasant surprises occur at a time down the road when a retiree can do little about it. Current investment returns are also tracked for an investor’s portfolio and added to the historical database upon which Monte Carlo simulations are made.

It is not necessary to have a financial planner to do a Monte Carlo analysis, however. You can find online Monte Carlo calculators by typing the words “Monte Carlo calculator” into an Internet search engine such as Google®. Most online analyses provide a short sentence or two that describes the probability of “success” (i.e., not running out of money). For example, “Success Rate: 46% chance that your investments will last 30 years.” Some calculators provide even more detail such as the average length of time that a portfolio will last and probabilities that savings would last between a range of time periods (e.g., between 25 and 30 years). It is important, however, to carefully review the assumptions upon which the results of Monte Carlo analyses are based. They can vary widely and result in different outcomes even with the same exact data.

The standard financial advice for someone planning on 30 years in retirement is to withdraw 4% of retirement savings in the first year of retirement (e.g., 4% of $500,000 is $20,000) and increase the withdrawal amount by 3% annually to keep pace with inflation. Using one Monte Carlo calculator, an analysis showed that, if someone retires with $1.5 million in retirement assets and withdraws 4% ($60,000) during the first year of retirement from a portfolio consisting of 50% stocks, 30% bonds, and 20% cash, savings is projected to last 34.12 years, on average, with a 95% probability of lasting between 28.42 and 39.82 years. Bump the annual withdrawal up to 5% ($75,000) and invested assets are projected to last an average of 32.03 years and fall between 21.74 and 42.33 years, a much wider range, 95% of the time.

Stated another way, the failure rate (i.e., probability of running out of money) is higher when the percentage of assets being withdrawn from a retiree’s investment portfolio increases. A high probability of failure, particularly when someone performs simulations using several online calculators and gets similar results, is a wake-up call and indicates that additional retirement “catch-up strategies” (e.g., working longer or moving to a less expensive home) may be in order to avoid outspending assets.

Given the relative ease of performing Monte Carlo analyses with historical investment data, as well as the “graying of America,” there has been an increasing amount of research during the past 15 years about sustainable retirement asset withdrawals. Academics and financial services firms alike have conducted studies about how long retirees’ assets will last. Monte Carlo analyses are the basis of much of this work.

Of course, past investment results, upon which Monte Carlo analyses are based, are no guarantee of future investment performance. Nevertheless, most experts caution against withdrawing more than 4% to 5% of invested assets (regardless of the amount) if you are concerned about making your money last a lifetime. In addition, to further increase the probability of making your money last, some investment advisors recommend forgoing annual inflation adjustments to retirement income withdrawals during extended market downturns and/or annuitizing a portion of invested assets to insure a lifetime income stream.

It is important to stress than Monte Carlo analysis is based on past investment results, which cannot be used to predict the future. Nevertheless, it is an important retirement planning tool and is widely considered to be superior to relying on historical averages to predict the future. The technique has been used for decades by scientists and in business scenario modeling and is now being widely used in personal finance. By calculating future probabilities, Monte Carlo analysis provides a realistic frame of reference for making retirement decisions, assuming realistic assumptions and correctly inputted data are used.

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