Average Return Calculator
Modify the values and click calculate
Periodic Returns
Geometric Mean (Annualized)
The geometric mean is always ≤ the arithmetic mean whenever returns vary from period to period (this gap is called volatility drag). It's the mathematically correct average for describing the actual compounded growth of a real series -- the arithmetic mean overstates it whenever returns are volatile.
Enter at least two yearly returns to see both averages.
Arithmetic Mean vs. Geometric Mean Returns
When an investment posts a different percentage return every year, "the average return" can mean two genuinely different numbers. This calculator takes a series of up to five periodic returns and computes both: the simple arithmetic mean, and the geometric mean -- the annualized rate that actually reproduces the same total compounded growth as the real sequence.
Arithmetic Mean: Simple, But Misleading
The arithmetic mean just adds up every period's return and divides by the count. It's easy to compute, but it silently assumes you could earn each year's return independently -- it ignores that gains and losses compound sequentially against a changing balance.
Geometric Mean: The Real Compounded Rate
The geometric mean takes the product of every period's growth factor (1 + return), takes the n-th root, and subtracts 1. This is the single constant annual rate that, compounded over the same number of periods, produces the identical ending value as the actual sequence.
Volatility Drag
The more a return series bounces around, the further the geometric mean falls below the arithmetic mean -- a gap known as volatility drag. A +50% year followed by a -50% year averages 0% arithmetically, but actually leaves you with a 25% loss overall (a -13.4% geometric/annualized rate).
Which One Should You Trust?
Use the geometric mean whenever you want to describe how an actual investment performed, or to project future compounded growth. The arithmetic mean is only appropriate for describing the average of independent, non-compounding single-period outcomes.
Worked Example
Suppose an investment returns 15%, 8%, -10%, and 22% over four consecutive years:
- Arithmetic mean: (15 + 8 - 10 + 22) / 4 = 8.75%.
- Geometric mean (annualized): (1.15 × 1.08 × 0.90 × 1.22)1/4 - 1 ≈ 8.06%.
The geometric mean is meaningfully lower than the arithmetic mean here -- that 0.69-percentage-point gap is the volatility drag from the -10% year interacting with the others. Over a real, compounding investment, 8.06% annualized is the number that actually reconciles with your account balance -- 8.75% does not.
Two Different Averages
- Arithmetic mean: 8.75%
- Geometric mean (CAGR): 8.06%
Why This Calculator Uses a Series, Not Two Values
If you only know a starting value and an ending value (with no visibility into the year-by-year path), that's a simpler question answered by the ROI Calculator's annualized ROI figure. This calculator is specifically for when you know the individual periodic returns and want to see how much they vary and how that variance affects the true annualized rate -- the multi-period series is the entire point.
Key Takeaways
- Geometric ≤ Arithmetic: Whenever returns vary, the geometric mean is always less than or equal to the arithmetic mean.
- Geometric Mean Is the "Real" Rate: It's the constant annual rate that actually reproduces your investment's real compounded outcome.
- Volatility Costs You: The more a return series swings, the bigger the gap between the two averages -- and the more misleading the arithmetic mean becomes.
- Just Have a Start and End Value? If you only know your total cost and final value with no periodic breakdown, use the ROI Calculator instead.