# The Monte Carlo method

April 1, 2002
The "Monte Carlo Simulation" is a technique used by mathematicians and engineers to find probable answers to highly complex and unpredictable equations like the stock market

By Rick Willeford, MBA, CPA/CFP

The "Monte Carlo Simulation" is a technique used by mathematicians and engineers to find probable answers to highly complex and unpredictable equations like the stock market. It can be used to determine how much you can realistically withdraw during retirement, and thus determine how much you need to have on hand. But I am getting ahead of myself ...

If you know the stock market (S&P 500) has averaged around a 12 percent annual return for the past 70 years, then any financial calculator can tell you how much money you need to have to retire with a certain annual withdrawal amount. Such a nice, neat answer is appealing, but it can be disastrously wrong!

Consider a doctor who retired in 1969. Based on average annual returns of 12.3 percent for the 40 years prior to his retirement, he thought an estimate of a 9.3 percent return was conservative. His calculator said he could withdraw \$70,000 of his \$1,000,000 nest egg per year for 30 years, including increases for inflation. However, as shown in Figure 1, he would have run out of money in 12 years – not 30! In reality, he should have only spent about \$41,000 per year. What happened?

He made the typical mistake of focusing only on the "average" annual return without considering when those returns occurred. In fact, over his 30-year time frame, the market would actually return an average of 13.9 percent – better than he had predicted. However, 1969 was a particularly bad time to retire because the stock market dropped and high inflation lay ahead. (Similarly, can you imagine someone retiring in 2000, just before the dot-com bubble burst?)

Although 12 percent is indeed a correct "average" annual return for the past 70 years, that does not address the pattern of returns for your specific 30-year plan. The ending value of a plan's projections is based on achieving the average return each and every year. It ignores market's ups and downs along the way.

Most sophisticated planners these days avoid giving an absolute withdrawal rate or dollar amount for retirement. Instead, they say something like, "Based on your portfolio, your plan of withdrawing, 5 percent plus an inflationary raise for the next 30 years has a 95 percent chance of success. If you withdraw 6 percent, the chances of your money lasting 30 years drops to 47 percent." In other words, it is important to know the probability that your plan will work. Enter Monte Carlo Simulation ("MCS") analysis. MCS is not perfect, but it introduces the concepts of volatility and timing risk.

Rather than use a simplistic "average return" approach, MCS randomly picks a different yet feasible return for each year for 30 years and sees how that scenario pans out. One such scenario is indeed arbitrary, but what if we did that 10,000 times! We would get a wide variety of results that show a trend. If 95 percent of the projected results accomplished the 30-year goal, then we might feel fairly confident. If only 50 percent worked out, then we should be alarmed and redesign the plan.

The figure above shows what a few of the 10,000 "trials" might look like. The dark line indicates a plan of withdrawals and portfolio mix that would give you a 95 percent chance of success, i.e., prevent your going negative before the end of 30 years. Based on your risk tolerance, you could adopt a more aggressive plan. This method has the distinct advantage, however, in giving investors the ability to make an informed decision.

Raymond "Rick" Willeford MBA, CPA/CFP, is president of Willeford & Associates, CPA, PC, a fee-only firm specializing in financial, tax, and practice-transition strategies for dentists since 1975. Mr. Willeford is president of the Academy of Dental CPAs, a member of the national Practice Valuation Study Group, and numerous dental study clubs. Contact him by phone at (770) 552-8500 or by email at [email protected].

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