The Power and Limitations of Monte Carlo Simulations

Explaining the past is much easier than predicting the future.  This uncertainty raises a significant number of issues when creating a financial plan for a client. Monte Carlo simulations will illuminate the nature of that uncertainty, but only if advisors understand how it should be applied – and its limitations.

The practical approach to creating the forecasted part of a financial plan has evolved over time. Estimates of future market returns were once based primarily on time value of money calculations. This approach is also known as deterministic modeling, whereby there is no randomness in the future outcome. For example, a financial plan would assume a long-term return on stocks of 10% for each year with no variability over time.

An alternative to – and improvement upon – deterministic models (like time value of money) is stochastic models (such as Monte Carlo simulations) that incorporate randomness into the modeling process. The use of Monte Carlo tools has increased considerably over the last decade, which can be attributed to lower computing costs, increased recognition that returns are random and the need to provide more robust financial plans to clients.

In most Monte Carlo tools, the returns and inflation are treated as random, and they vary based on an assumed mean, standard deviation and correlation. Those inputs are defined by the user and have a considerable impact on the results of any simulation. If you were to set the standard deviations to zero in these types of models, you would effectively run a deterministic simulation, because each return would be assumed to be known with absolute certainty and there would be no assumed variability in the forecast.

User error

Monte Carlo simulation has received a lot of criticism, though not always for valid reasons. One common criticism is that such tools may not incorporate the “fat tailed” nature of return distributions, as well as things like autocorrelation (which is when returns of a variable, like inflation, are correlated over time).

But this argument is like saying all cars are slow. There are no constraints to Monte Carlo simulation, only constraints users create in a model (or constraints that users are forced to deal with when using someone else’s model). Non-normal asset-class returns and autocorrelations can be incorporated into Monte Carlo simulations, albeit with proper care. Like any model, you need quality inputs to get quality outputs.