How are average returns and standard deviation calculated?
See how average returns and standard deviations are calculated in the app and what settings affect these values.
Last published on: October 31, 2025
| Setting | Possible Values |
|---|---|
| Analysis Method | Historical, Traditional Monte Carlo, Regime-Based Monte Carlo |
| Fees & Expenses | Asset class fees, overall fee |
| Capital Market Assumptions | Average annual real return and standard deviation for each asset class, correlations between asset classes |
| Asset allocation | % of each asset class, summing to 100% |
You can find a plan's Analysis Method in the plan's Advanced Settings (in the Plan Analysis section).
For Monte Carlo analysis methods, average returns are the asset-class-weighted average of the expected net real returns of each asset class. Standard deviations are calculated as the square root of the portfolio variance. The formula for portfolio variance of a two-asset portfolio is shown below (where w = asset weight). For portfolios with more than two assets, the formula is extended (but is too complex to show here).
The Regime-Based Monte Carlo analysis method has two sets of capital market assumptions - one for the near-term and one for the long-term. By default, the near-term is the first 10 years of a plan, but this can be changed by the user. When using Regime-Based Monte Carlo, the app displays expected return and standard deviation for the near-term period.
Average Returns when using the Historical Analysis Method
When using the Historical analysis method, the app reports the average net real return and standard deviation of a mix of historical index returns over all available history, based on the asset allocation for the account or portfolio in question and adjusted for fees included in the plan. (Related: What indices does Income Lab use to model asset class returns?).
The available history used to calculate historical averages and standard deviations depends on the "Economic Context" setting for the plan. Economic context filtering removes from the historical calculations periods that are least similar to the present in economic terms. (Related: What economic indicators does Income Lab track?) You can see this economic context by viewing the Historical Analysis graph for a particular plan. Periods shaded in grey on this graph are least like the present. Those marked in blue are more like the present.
In this example, the historical averages will include periods beginning in the 1960s and 1970s but exclude periods beginning in the 1980s and 1990s.
If you would like to remove this economic context filtering, simply move the Economic Context slider to the left and click Apply new Economic Context to plan.
