Planning Your Retirement Using The Monte Carlo Simulation

By Mark P. Cussen, CFP®, CMFC, AFC | December 20, 2012 AAA

The city of Monte Carlo in the country of Monaco has long served as a playground for the jet set, where rich gamblers who can afford to lose huge sums of money come to play for big stakes in games of random chance where strategy and experience can provide little or no benefit. But those who are trying to plan for a secure retirement and can't afford to lose their savings don't want to take big chances with their money.

How It Works
Although naming this type of calculation after a gambling mecca may seem a bit ironic, it has come to be used in the financial arena to signify a planning technique used to calculate the percentage probability of specific scenarios that are based upon a set group of assumptions and standard deviations. This method of calculation has often been used in investment and retirement planning to project the likelihood of achieving one's financial or retirement goals and whether or not a retiree will have enough income to live on for life, given a wide range of possible outcomes in the markets. While there are no absolute parameters for this type of projection, the underlying assumptions for these calculations typically include such factors as interest rates, the client's age and projected time to retirement, the amount of the investment portfolio that is spent or withdrawn each year and the portfolio allocation. The computer model then runs hundreds or thousands of possible outcomes using actual historical financial data. The results of this analysis usually come in the form of a bell curve, where the middle part of the curve delineates the scenarios that are statistically and historically the most likely to happen while the ends, or tails measure the diminishing likelihood of the more extreme scenarios that could also occur.

Limitations
Despite its apparently thorough mathematical breakdown of possible future outcomes, recent market turbulence has served to expose a major weakness that seems to afflict this method of financial projections. While its supporters are quick to 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 methodology were not shown a real possibility of market performance such as we have had over the past few years.

In his paper, The Retirement Calculator from Hell, William Bernstein clearly 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 represents a loss of 10%. If you start with a $1,000,000 portfolio and toss the coin once a year for 30 years, you will end up with an average annual total return of 8.17% over that time. That means that you could withdraw $81,700 per year for 30 years before exhausting your principal. If you were to flip tails every year for the first 15 years, however, you would only be able to withdraw $18,600 per year, while if you were lucky enough to flip heads the first 15 times you could take out a whopping $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 portfolio of one million dollars that was invested in five different combinations of large and small cap stocks and five-year treasuries back in 1966. That year marked the beginning of a 17-year stretch of zero market gains when you factor 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 for the full 30 years.

How Can I Plan Realistically Instead?
There are a few basic adjustments that experts suggest can help remedy the shortcomings of the 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 percent. 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
There is no absolutely foolproof way to predict what will happen in the future. But running a Monte Carlo analysis that allows for the real possibility of disaster can give you a clearer picture of how much money you can safely withdraw from your retirement savings. For more information on Monte Carlo simulations, visit http://www.moneychimp.com/articles/volatility/retirement.htm or http://www.flexibleretirementplanner.com/wp/ or consult your financial advisor.

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