In our last post, we introduced a new calculator to help you forecast your retirement savings. Part of this introduction showed you how the uncertainty in the markets may affect your savings forecast. So here, we summarize the differences between the two simulation options available in our new retirement savings calculator: bootstrapping and geometric Brownian motion.

Why use simulation?

Simulation, or often termed “Monte Carlo” simulation, is a scientific method to model future uncertainty using a random number generator. In the case of our savings calculator, it models the uncertainty of annual stock and bond returns. By running many simulation trials, each trial can represent one of many possible outcomes for investment returns over your planning horizon. Then, you can see what risk you may be taking in assuming a more pessimistic or optimistic account balance at retirement. For example, using default inputs to our model, a retiree can expect their future tax-deferred account balance to be likely more than $629,047, but likely not more than $1,073,058. (These values are based on default 25th and 75th percentiles. Our calculator allows these levels to be adjusted.)

Bootstrapping

The two most common approaches to simulation are bootstrapping and geometric Brownian motion. Bootstrapping uses historical returns of stocks and bonds, and randomly samples from them for each trial to develop simulated returns. For our model, we reconstructed annual returns for an S&P 500 ETF and aggregate bond ETF from 1989 to 2021. We used the same methodology described by DiLellio (2018). Retirees benefit from using bootstrapping since it preserves the historical distribution of stock and bond returns, as well as the correlation of their returns. In particular, extreme market shocks, like the financial crisis of 2008-2009, the dot-com bubble burst of 2001, and the Covid-19 pandemic of 2020 are all included when simulation uses bootstrapping.

One approach to simulating future returns is termed bootstrapping, where we simulate returns by random selection from a set of historical returns. In our calculator, we use annual returns from an S&P 500 and aggregate bond index ETF from 1989 to 2021. This approach has the benefit that it accurately represents the past, including the large market corrections in the financial crisis of 2008-2009, the dot-com bubble bursting in 2001, and the global pandemic in 2020. You can read more about this simulation approach in this peer-reviewed research in DiLellio (2018).

Geometric Brownian Motion

However, what if the future isn’t entirely represented by the past? In this case, we can use the geometric Brownian motion (GBM) stochastic process to simulate future stock and bond prices. Why? Using a GBM permits you to dictate return behavior using a normal distribution of asset returns. This simulation approach gives the retiree complete control over future returns. And, the retiree can select volatility and correlations of stock and bond returns. Lastly, GBM is the foundation for the famous Black-Scholes Option pricing formula. Unfortunately, GBM does not capture extreme events well. The image below from DiLellio (2018) shows how the normal distribution does a fair job, but not a perfect one, of fitting stock and bond returns.

So, which simulation approach is better?

The short answer is “it depends”. Like any mathematical model, they both have their own strengths and limitations. Fortunately, you can use either of these models to develop your savings plan. In fact, we hope you consider using both, to best understand the risk of achieving your savings goals!