Understanding Arithmetic vs. Geometric Mean
The difference between arithmetic and geometric mean values can be illustrated simply:
If a house grows in value from $100,000 to $150,000 over 10 years, the total increase is 50%.
Arithmetic mean: 5% per year
Geometric mean: ~4.14% per year
This shows an important point: the arithmetic mean is always equal to or higher than the geometric mean.
Why This Matters in Client Planning
When creating client plans with asset allocations, the assumed long-term “mean” returns can be arithmetic or geometric:
Arithmetic mean assumptions tend to overestimate returns because they ignore compounding and volatility. For example, a $100k property growing at 5% per year consistently would be worth ~$163k after 10 years, higher than the actual $150k.
Geometric mean assumptions reflect compounding, providing a more realistic picture for steady growth scenarios.
In practice:
For standard cash-flow projections (assuming consistent year-on-year returns), geometric mean values are ideal.
For Monte Carlo simulations, where returns are randomized, arithmetic mean values are better. Volatility drag in the simulation naturally reduces the effective return, narrowing the gap between arithmetic and geometric values.
How Our Software Handles This
To balance these needs, we recommend:
Use arithmetic mean values for your assumptions.
In Preferences > Market Assumptions, enable “Approximate Geometric Mean for default calculation.”
This tells the software to adjust your arithmetic mean values to approximate geometric means using a standard formula:
Where:
G = Geometric mean
R = Arithmetic mean
V = Variance (SD²)
Note: Simply selecting arithmetic vs. geometric does not change projections. A visible difference appears only when this correction is applied, reducing the overstatement inherent in arithmetic assumptions.
Where You Can See the Impact
After enabling the correction, you can observe differences in:
Year View > Investments/Pensions/Retirement – actual rates of return applied.
Plan Settings > Asset Allocation – assumed mean returns for individual accounts.
Monte Carlo Simulations
When running a Monte Carlo simulation:
The software automatically disables the geometric correction.
Monte Carlo introduces volatility, which naturally reduces returns (volatility drag).
Applying the geometric correction here would “double-correct” for volatility, so it’s unnecessary.
Key Takeaways
Use the approximate geometric mean adjustment for standard projections to prevent overestimating returns.
Use arithmetic mean values for Monte Carlo simulations; volatility drag already adjusts for the difference.
This ensures projections are realistic for standard scenarios while Monte Carlo simulations reflect market variability.
Illustrative Example:
| Method | Annual Rate | Final Value (10 years) |
|---|---|---|
| Arithmetic mean | 5% | ~$163,000 |
| Geometric mean | 4.14% | $150,000 |
Summary:
Arithmetic mean overestimates returns in steady scenarios.
Geometric mean corrects for compounding.
Monte Carlo simulations naturally account for volatility → no geometric correction needed.
Our software automatically applies the correction for standard projections and disables it for Monte Carlo runs.