The Monte Carlo analysis methods in the Income Lab app produce monthly returns and inflation rates that are independent and identically lognormally distributed (i.i.d). In other words, we don’t inject any assumptions about non-normal skewness or kurtosis ("fat tails"). Similarly, we do not model any autocorrelation in returns or inflation. (Negative autocorrelation would be used to model "reversion to the mean".) We certainly recognize that this may be overly simplistic, but we stick to this simpler approach for two reasons, one analytical and the other practical:

Analytical

When we apply statistical tests to historical monthly market returns and inflation, we have been unable to prove that these returns are NOT normally distributed. (If you’re interested, we apply the Shapiro-Wilk and Shapiro-Francia tests.) We do recognize that some academics and analysts do have arguments – maybe even good ones – that monthly returns are not normally distributed, or that there is evidence for autocorrelation, but…

Practical

If we modeled non-normal skewness, excess kurtosis (fat tails), or autocorrelation, users would have to enter/edit these parameters or accept our defaults. Usually, firms don’t have assumptions for these parameters or ways to audit tens or hundreds of default capital market assumptions for autocorrelations, such as multiple lags, skewness, and excess kurtosis, so users may be at a loss. So, the practical cost of adding this complexity would be very high, and the simpler approach is certainly reasonable and widely used.

If you are interested in modeling reversion to the mean in Income Lab, you may wish to use either the "Historical" or "Regime-Based Monte Carlo" analysis methods. In the latter, specifying different near-term and long-term capital market assumptions will have the effect of altering a return's behavior as the plan progresses (for example, from lower expected returns to higher returns).