The simulator offers three methods for modeling investment returns, selectable directly on the simulation chart: Monte Carlo and Historical Simulation are stochastic - they generate many different return sequences to produce a range of outcomes - and Linear is deterministic. This article covers the two stochastic methods; Linear is described at the end.

Monte Carlo mode generates returns by drawing from a statistical distribution for each year independently. The center of that distribution is your assumed average return, and the width is controlled by the standard deviation parameters in the Simulation Parameters section. Each year's stock and bond returns are generated together using the correlation coefficient, so years where stocks do poorly tend to coincide with years where bonds perform differently in the expected way. This approach is mathematically clean and widely used in financial planning software.

Historical Market Simulation mode (also called block bootstrapping) generates returns by sampling real historical market data from 1872 through 2025. Instead of drawing one year at a time, it draws contiguous multi-year blocks - sequences of consecutive years taken intact from history. This preserves real-world patterns like multi-year bear markets followed by recoveries, the 1970s stagflation decade, or the dot-com crash unfolding over several years. Because the blocks are actual historical sequences, the natural correlation between stocks and bonds during each period is preserved without needing a separate correlation parameter.

Block length defaults to 4 years and is adjustable from 1 to 15 in the Simulation Parameters section of Assumptions. Shorter blocks (1-2) create more randomized combinations of historical years and break up the multi-year regimes; longer blocks (5+) preserve more of those regimes - bull markets, recessions, inflation periods, and bond-rate environments - at the cost of fewer distinct sequences in the sample. Block length 1 is equivalent to random-year bootstrap sampling. The default of 4 is a balance between preserving short-term sequencing and keeping the sample diverse.

In Historical Market Simulation mode, the historical returns are scaled to align with your assumed return rates. This is done by computing the average log return of the historical record for stocks and bonds separately, then shifting every year's log return up or down by the difference between your assumed return and that historical average. The result is then converted back to a simple annual return. This means the entire distribution moves to be centered on your assumptions - the shape, sequencing, and year-to-year variation of the historical record are preserved, but the level is anchored to whatever stock and bond return averages you have set on the Assumptions page. In Monte Carlo mode, the arithmetic mean of the distribution is set to your assumed return, but because volatility drag reduces compound returns over time, the actual long-run compounded return will be somewhat lower than that assumption - an inherent property of any distribution with non-zero variance.

The practical difference is in the extremes. Monte Carlo mode produces a smooth, symmetric distribution of outcomes. Historical mode can produce more severe crashes and longer recoveries because real markets have experienced events that fall outside what a statistical distribution would predict. Neither mode is definitively more accurate - they represent different modeling philosophies, and comparing results across both can be a useful way to stress-test your plan.

Linear mode is different in kind from the other two. Instead of many random sequences, it applies your expected average return every single year, with no variance, producing one smooth deterministic "straight-line" projection rather than a range. Because there is only one path and no randomness, the probability-based readouts - success rate, risk of ruin, and the 20th / 80th-percentile outcome tiles and confidence band - do not apply and are hidden in this mode, and the outcome tile is relabeled "Projected Outcome". Linear is useful as a quick sanity check ("what would I have if returns were perfectly steady?"), but it paints a rosier picture than markets usually deliver, because a constant-return line leaves out both volatility drag and sequence-of-returns risk. If you want that straight line without leaving the realistic view, the Monte Carlo chart has a steady-return reference line that overlays it on the median instead.