Monte Carlo simulation is a modelling technique that’s useful in many areas, including physics, engineering and finance. If a process depends on multiple random variables, it can be impossible or impractical to calculate the odds of different outcomes. The Monte Carlo approach assigns values to each random variable and assesses the outcome. It doesn’t do this just once, but typically thousands of times. It then draws conclusions from all results together.

In retirement planning, Monte Carlo is often the approach advocated by professionals. But it’s understandably less well understood by the public at large. Let’s take a look at the other main approaches before turning back to Monte Carlo.

## Planning based on averages

If you pick an online retirement calculator at random, chances are that it will be based on averages. For example, it might assume average investment growth of 7% per year. When projecting your retirement fund, the tool would then assume that it would grow by 7% every year. Proponents of this approach would argue that over many years any real-life fluctuations should cancel each other out. They’d make the same argument for the rate of inflation. Even though it’s not the same every year, why not pick a sensible average and use that?

The problem with this approach is that fluctuations *don’t *necessarily cancel each other out. They can even reinforce each other, for example during a bear market. Ideally, your retirement fund should be at its maximum close to your retirement date; and that’s the time when a major market setback could have the most lasting impact. The further you project into the future, the less reliable your projections become, not more reliable. Weather forecasters know this all too well: long-range forecasts are the least reliable.

Another assumption that typical (non Monte Carlo) retirement planning tools make is about how long your retirement will be. Of course, this depends on how long you’ll live. So you have to pick a number. You might pick your average life expectancy for your age and demographic. But then there’s a 50-50 chance that you’ll live longer, which means you might outlive your forecast funds.

## Using historical market data

Rather than assuming average investment returns, some more sophisticated retirement planning tools base their projections on historical market data. Such data could include stock prices, bond prices as well as inflation rates. The data would typically go back at least 100 years. Say you want to project investment growth over the next 30 years. You’d try out all the possible 30-year periods covered by the historical data. For example, if 130 years of data were available, which is in the right ballpark, there’d be 100 such periods, or scenarios. The idea is that if your retirement plan would have been successful during all 100 scenarios, then it should be safe for the future.

Just like Monte Carlo simulation, this approach looks at multiple outcomes, not just averages. Proponents argue that it’s rooted in reality, and is therefore superior to Monte Carlo simulation. However, there are a number of significant limitations and drawbacks:

- The past is not always a reliable guide to the future. There may be factors rooted in the present that one might reasonably expect would affect future outcomes.
- In the example there were just 100 scenarios. This is an extremely small number of statistical samples. Other things being equal, the margin of error is 10 times bigger than in a Monte Carlo simulation of 10,000 trials.
- The scenarios are not independent of each other, as they follow on from each other. This increases the margin of error still further.
- You can’t apply historical data to life expectancy, since each person only has one life.

The historical approach is superior to just using averages, but its drawbacks shouldn’t be ignored.

## Using Monte Carlo Simulation

Rather than assuming that the future of markets and investments will be similar to the past, the best approach is to derive a statistical model that’s consistent with the past. It needs to have configurable assumptions, which should take into account not just the past, but the present economic and geopolitical landscape. Rather than assuming a fixed life expectancy, you should treat longevity as one more random variable; not completely random of course, but consistent with demographic information.

Then apply Monte Carlo simulation to the model using not hundreds, but thousands of scenarios. In some scenarios you might live a long time, in others only a short time. Some scenarios may see a string of badly performing years just after retirement; others may show excellent growth. A reasonable number of scenarios is around 10,000. This should be enough to know how good or bad your plan is. The caveat is that Monte Carlo simulation is only as good as the underlying assumptions; for this reason going beyond 10,000 scenarios is likely to be overkill.

## Results of Monte Carlo simulation

Once you’ve run a Monte Carlo simulation, the question then becomes how to interpret the results. Suppose it tells you that you have a 10% chance of running out of money. Is that good or bad? That will be partly subjective, depending on your own attitudes. But there may be nuances that would make an objective difference. For example, it might be that in the vast majority of the 10% failures you ran out of money within a year of dying. That would suggest that small changes in spending along the way could have avoided running our of money. On the other hand, if in most of the 10% you ran out of money more than 5 years before you died, then your plan would look a bit shakier.

Another thing to consider is whether or not you assumed a constant or variable level of discretionary spending. If you assumed constant spending, then there’s more scope to take corrective action. If you assumed variable spending, then presumably some adjustments would have already been made, so there’d be less scope for further corrective action. Some planners suggest that very high failure rates are acceptable, provided you’re willing and able to make adjustments.

In our own retirement planning tool, we’ve drawn inspiration from many industry sources. By itself, Monte Carlo simulation is merely a way to evaluate how good or bad your plan is, important as that is. But in addition to that, and uniquely, EvolveMyRetirement® will help you optimise your plan, taking uncertainty into account.

Although Monte Carlo simulation isn’t a silver bullet, if you use it correctly it’s the most reliable tool for projecting your retirement plan.