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Monte Carlo Simulation

BLOG, EDUCATION  |  24 Jun 2010

If you are a client of ours, you have probably heard us at one time or another talk about Monte Carlo Simulation (or Monte Carlo Analysis). The term itself is kind of strange sounding, and the first time you hear it you’re bound to conjure up images of either the famous casino in Monaco or a two-door Chevy coupe. Believe it or not, the former image would be more correct, but I’ll explain that later. Monte Carlo simulation is a calculation method used in a wide variety of fields ranging from physics, weather forecasting, architecture, and of course financial planning. Its purpose is to estimate the probability of a certain outcome using random input numbers. In most cases, thousands or even tens of thousands of calculations are made in order to produce the result. The advent of today’s high-speed computers has made it possible for these calculations to be done quickly and has made it possible for small companies like ours to use Monte Carlo simulations.

Have I lost you yet? Let me try to bring you back by telling you how we use Monte Carlo analysis. Most of our clients are very interested in knowing if they are on track to live the lifestyle that they desire. Whether they are retired with their earning days well behind them, or they are just entering their peak earning years, Monte Carlo analysis is one of several tools we can use to provide them with some guidance on what their future might look like. In its simplest application, we can us it to calculate the probability that someone’s nest egg will last a given number of years assuming that person is drawing on that nest egg at a given annual amount. Monte Carlo analysis will produce that probability using projected market returns that reflect the investment composition of the nest egg. But instead of simply applying the portfolio’s average historical return, the analysis will arrange the annual returns in a random fashion so that one year the portfolio might return 6% and the next year it might return -3%. (It is this random generation of results that led the creators of Monte Carlo simulation to name it after the casino where roulette is so popular.) The possible range of investment returns applied to the simulaton will depend upon the risk profile of the portfolio. More aggressive portfolios will have a wider range of possible returns, while the range on more conservative portfolios will be narrower. To provide a more reliable figure, the calculations are done thousands of times. The idea is to simulate what happens to the nest egg by running multiple scenarios using the entire range of expected investment returns.

Now, the previous example doesn’t really reflect a real-life situation for most people. First of all, almost no one spends the same amount of money every year. Also, the composition of your portfolio in most cases changes as you get older to a more conservative asset allocation. Fortunately, we are able to account for these things in our analysis. Modern software also allows us to take other real-life variables, like inflation, into account, because after all inflation can have as much impact on the success of a plan as investment return can. Better versions of the Monte Carlo analysis allow the user to factor in the effects of bad timing of returns to account for the fact that a couple of bad years in a row can have a larger or smaller impact on the success of a plan depending on when they occur. Perhaps the most serious limitation of Monte Carlo is its inability to effectively account for high impact events which are outside the realm of what is thought to be possible, otherwise known as “Black Swan” events. The market crash of 2008 certainly qualifies as such an event. Its difficult to build these types of events into the Monte Carlo model, but after 2008 software vendors are making an effort.

If the simulation for a particular person indicates the probability of success at say 65%, we may consider a number of steps to take in order to increase the odds. Usually those steps will include more saving, less spending, or perhaps working a little longer than they had planned. Another option would be to consider increasing the risk profile of the portfolio by adding more exposure to stocks, but we are usually hesitant to ask anyone to step out of their risk tolerance comfort zone.

Monte Carlo Simulation is not perfect, but we believe it is a useful tool in financial planning to offer some guidance on the probable success of a plan. It would be great if it could predict the future, but it can’t, and we make certain to tell our clients about its limitations. For instance, we cannot predict tax rates with any degree of certainty, and attempting to apply probabilities to tax rates does not make much sense mathematically. Yet tax rates have a definite impact on any financial plan. Also, Monte Carlo simulation does not take into account human behavior. After a particularly good year of investment returns, many people would likely spend a little more money the following year than they normally would, and this is not taken into account. Ultimately, the percentage number that a Monte Carlo simulation spits out is only as good as the data that’s entered to arrive at that percentage. In order not to create unrealistic expectations, we run the simulations using conservative investment returns and liberal inflation numbers.

Finally, we know that financial plans must be viewed as living organisms that are constantly changing and evolving. Whenever Monte Carlo simulations are used in financial planning, they should be revisited regularly to account for real-life changes. They also must be viewed for what they really are; a useful but imperfect guide that should never be relied upon as the sole analysis tool of anyone’s financial plan.