Glossary term
Geometric Average Return
Geometric average return is the compounded average return that produces the same ending value over multiple periods.
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What Is Geometric Average Return?
Geometric average return is the compounded average return that would produce the same ending value over multiple periods. It accounts for the fact that investment gains and losses compound over time.
For multi-period performance, geometric average return usually gives a more realistic picture of investor experience than a simple arithmetic average.
Key Takeaways
- Geometric average return measures compounded performance over multiple periods.
- It uses growth factors rather than simply adding returns.
- It is usually lower than arithmetic average return when returns fluctuate.
- It is closely related to compound annual growth rate.
- It helps show the return path an investor actually experienced.
Geometric Average Return Formula
In this formula, R1, R2, and Rn are the returns for each period. n is the number of periods. Each return is converted into a growth factor, such as 1.10 for a 10% gain or 0.90 for a 10% loss.
Geometric vs. Arithmetic Average Return
Measure | Calculation idea | Best use |
|---|---|---|
Arithmetic average return | Add returns and divide by count | Simple average period return. |
Geometric average return | Compound growth factors | Actual multi-period performance. |
CAGR | Geometric return over annual periods | Annualized beginning-to-ending growth. |
Example
If an investment gains 20% and then loses 20%, the arithmetic average return is 0%. But the investment does not break even. A $100 investment becomes $120 and then falls to $96.
The geometric average return captures that compounding effect. It shows that volatility can reduce the compounded result even when the simple average return looks fine.
Why Volatility Changes the Answer
Geometric average return falls as return variability increases because losses and gains do not offset symmetrically. A 50% loss requires a 100% gain to recover, so uneven returns drag down the compounded path.
This is why the geometric average is usually lower than the arithmetic average when returns fluctuate. The larger the swings, the larger the gap tends to be.
Cash Flows and Timing
Geometric average return assumes a linked return path without adding or removing money inside the measurement period. If an investor contributes or withdraws cash along the way, a money-weighted return or internal rate of return may be more appropriate.
That distinction matters for personal performance reports. A fund's geometric return and an individual investor's realized return can differ if the investor bought or sold at different times.
Where It Is Most Useful
Geometric average return is most useful when measuring performance over linked time periods. It is commonly used for fund returns, portfolio performance, strategy backtests, and growth-rate comparisons.
It is less useful for estimating a single-period expected return. For that use, arithmetic average return may be more appropriate depending on the model.
The Bottom Line
Geometric average return is the average that respects compounding. It is the better measure when the question is what return an investor actually earned over multiple periods.