Rolling the Dice

Adam M. Grossman

IN JANUARY 1946, a man named Stanislaw Ulam found himself confined to a hospital bed, having suffered an encephalitis attack. A brilliant scientist and a veteran of the Manhattan Project, Ulam wasn’t the type to sit idly while he recuperated. Instead, after playing innumerable games of solitaire to pass the time, Ulam began to examine the statistical aspects of the game.

Among the questions he asked: How can you accurately estimate the probability of winning a game? To answer this question, Ulam ended up devising a novel statistical technique that he dubbed Monte Carlo analysis. Today, this approach is broadly accepted and widely used in everything from engineering to biology to financial planning to meteorology—and even basketball.

How exactly does Monte Carlo analysis work? The idea is this: As long as you know the basic dynamics of how something works—whether it’s weather patterns, card games or anything else—you can use a computer to simulate an experiment thousands of times and then simply count up the frequency of various outcomes.

How is Ulam’s technique applied to financial planning? Knowing how the stock market has performed in the past, and the degree to which it varies from year to year, you can simulate the market’s future performance. But instead of focusing on the stock market’s average annual return, Monte Carlo analysis focuses on average multi-year returns. This allows financial advisors to reassure their clients with confident-sounding statements such as: “I’ve tested 10,000 scenarios and can tell you that your retirement plan has a 90% probability of success.” To see what a Monte Carlo simulation looks like, check out Vanguard Group’s retirement nest egg calculator.

While Monte Carlo analysis is widely used in financial planning, I would advise caution, for two reasons:

1. Subjective inputs. Monte Carlo simulation works well when forecasting physical or mechanical processes—things that act in predictable ways or, at least, within known limits. A card game, for example, can develop in numerous ways. Still, it’s always played with a fixed set of rules and an identical deck of cards. While you don’t know which card will come up next, you do know there will never be five aces in a deck. As a result, the set of possible outcomes is necessarily limited.

When it comes to the stock market, though, the opposite is true: An infinite combination of political and economic events—coupled with human emotions—can drive the market in unpredictable ways. In a card game, it’s difficult to know what will happen next. In the stock market, it’s impossible to know. And it’s not just the stock market. Lots of other variables impact the success of a retirement plan, including inflation, tax rates, interest rates and potential changes to Social Security and Medicare.

Try this thought experiment: Tomorrow morning, pick up the newspaper and ask yourself, “How many of these stories could I have predicted five or 10 years ago?” Not many, I suspect—and yet that’s what we are doing when we expect Monte Carlo analysis to help us forecast multi-decade retirement scenarios. To be sure, the past serves as a guide to the future, but it’s just a guide. That’s why any simulation of the stock market rests on shaky ground, simplistically assuming that the future will mirror the past.

2. Less-than-useful output. If the inputs to a Monte Carlo analysis are subjective, the outputs are even more troubling.

First, Monte Carlo output is normally expressed as a percentage—a 90% probability of success, for example—but what exactly does “success” mean? It means simply that you won’t run out of money. That sounds logical. Problem is, it’s defined very literally. If a Monte Carlo simulation determines that there will be even $1 left at the end of someone’s life, that is defined as success. For a computer, that may make sense. But for a real person seeing their funds rapidly approach zero late in life, that hardly sounds like a pleasant or successful outcome. But because this is the way Monte Carlo simulations work, they may lull people into a false sense of security or, alternatively, scare the daylights out of them, when neither reaction may be warranted.

The second problem with Monte Carlo output is that, if you dig into the results, it provides a range of potential outcomes so wide that it borders on the absurd. Use a typical Monte Carlo program to simulate the growth of a $1 million portfolio over a 30-year retirement, for example, and it will unhelpfully project that your assets will fall somewhere between zero and $29 million. While this may be statistically accurate, personally I don’t find it very useful.

To be sure, Monte Carlo analysis has its place in scientific disciplines. But when it comes to retirement planning, I would urge you to be skeptical. Always look at the numbers behind the numbers—and never let any one analysis drive your financial decisions.

Adam M. Grossman’s previous articles include Get a LifeHigher Taxes and Moving Target. Adam is the founder of Mayport Wealth Management, a fixed-fee financial planning firm in Boston. He’s an advocate of evidence-based investing and is on a mission to lower the cost of investment advice for consumers. Follow Adam on Twitter @AdamMGrossman.

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