Average return calculator
Arithmetic and geometric average of yearly returns, with volatility and growth of a starting sum.
About the average return calculator
Arithmetic and geometric average of yearly returns, with volatility and growth of a starting sum.
Part of SmartCalcy’s investing & savings tools. It runs in your browser with no account, uses your own currency and units (change them at the top of the page), and gives estimates for information only, so check official guidance before you rely on a result.
How to use the average return calculator
What it calculates and when to use it
Averages a series of yearly investment returns and shows the difference between the simple average and the compound average, which is the one that matches what your money actually earned.
How to use it, step by step
- Enter the starting value.
- Enter each year’s return as a percentage, using a negative number for a loss.
- Add or remove years.
What each input means
- Yearly return – The percentage change in that year, including losses.
How to read the results
- Arithmetic average – The simple mean of the returns.
- Geometric average – The compound yearly rate that gives the same final value.
- Volatility – The sample standard deviation of the returns.
The formula
Geometric average = (Π (1 + rᵢ))^(1 ÷ n) − 1. Arithmetic average = Σ rᵢ ÷ n. Volatility = √(Σ (rᵢ − mean)² ÷ (n − 1)).
A worked example
Returns of 12%, −8%, 15%, 6% and 9% have an arithmetic average of 6.8% but a geometric average of 6.48%. 10,000 grows to 13,691.03, a total return of 36.91%, with a volatility of 8.93%.
Assumptions and limits
- Annual returns are shown after charges only if you enter them that way.
- Past returns do not predict future returns.
Common mistakes
- Using the simple average to project growth. It overstates compound returns.
- Entering −100% or worse, which wipes out the investment.
Frequently asked questions
Why is the geometric average lower?
A loss reduces the base on which the next gain is earned, so volatility drags down compound growth.
Related tools
Details
- Arithmetic average
- 6.8%
- Geometric (compound) average
- 6.48%the rate that gives the same final value
- Total return
- 36.91%
- Volatility (standard deviation)
- 8.93%
- Final value
- £13,691.03
- Best and worst year
- 15% / -8%
Value after each year
| Year | Return | Value |
|---|---|---|
| 1 | 12% | £11,200 |
| 2 | -8% | £10,304 |
| 3 | 15% | £11,850 |
| 4 | 6% | £12,561 |
| 5 | 9% | £13,691 |