How the Average Return Calculator Works
"Average return" sounds simple, but it can mean two different numbers, and they can be far apart. One is the simple average, where you add up the yearly returns and divide. The other is the annualized return, which is the steady yearly rate that would give you the same result. The Average Return Calculator shows both, so you can see how an investment really performed.
What you enter
You choose one of two ways to enter your investment:
- I know the start and end value: enter the amount you started with, the value at the end, the years you held it, and any income you took out on the way, such as dividends or interest.
- I know the return of each year: enter the amount you started with and the return of each year in percent, separated by commas. Use a minus sign for a loss.
How the results are worked out
total return = (end value + income - start value) / start value simple average = total return / years annualized return = (end value + income) / start value, to the power of 1 / years, minus 1
With yearly returns, the calculator multiplies the years together, because each year's return applies to the money you have at that time:
growth = (1 + r1) x (1 + r2) x ... x (1 + rn) annualized return = growth ^ (1 / n) - 1 simple average = (r1 + r2 + ... + rn) / n
The annualized return is also called the compound annual growth rate, or CAGR. It is the better measure of what happened to your money.
Example 1: start and end value
You invested $10,000, and five years later it is worth $15,000. You took out no income.
| Result | Amount |
|---|---|
| Total return | 50.00% |
| Simple average per year (50% / 5) | 10.00% |
| Annualized return | 8.45% |
| Gain | $5,000.00 |
The simple average says 10% a year, but 10% a year for five years would give $16,105, not $15,000. Only 8.45% a year, compounded, gives exactly $15,000. So the annualized figure is the honest one.
Example 2: uneven years
You invested $10,000. The yearly returns were +10%, -20%, +15%, +8% and +12%.
| Year | Return | Worth at the end |
|---|---|---|
| 0 | start | $10,000.00 |
| 1 | +10% | $11,000.00 |
| 2 | -20% | $8,800.00 |
| 3 | +15% | $10,120.00 |
| 4 | +8% | $10,929.60 |
| 5 | +12% | $12,241.15 |
The simple average is (10 - 20 + 15 + 8 + 12) / 5 = 5.00%. But your money grew by only 22.41% in total, which is an annualized 4.13%. The gap of 0.87 percentage points comes from the bad year. A loss hurts more than an equal gain helps: after a 20% fall, you need a 25% rise to get back to where you were.
Chart: the return of each year
Year 1 +10% ██████████ Year 2 -20% ████████████████████ (loss) Year 3 +15% ███████████████ Year 4 +8% ████████ Year 5 +12% ████████████
The calculator draws these as green bars for gains and red bars for losses, and adds a line that shows how your money grew.
Why the simple average is too high
The simple average is always at least as high as the annualized return. They are equal only when every year has the same return. The more the years jump around, the bigger the gap. The calculator shows how much your years vary (the standard deviation) so you can see this. Two investments can have the same simple average, but the steadier one leaves you with more money.
Tips
- Use the annualized return to compare investments. It matches what you actually earned.
- Compare the same time span. A five-year figure and a twenty-year figure tell you different things.
- Count the income. Dividends and interest are part of the return. Add them in the income box if you took them out.
- Watch for money added or removed. If you added money during the years, this calculator cannot tell your gains from your deposits. Use a calculator for return with regular deposits instead.
What this calculator does not include
- Fees, taxes and inflation. Your real return after these is lower.
- Deposits or withdrawals during the period, except the income you enter.
- Any prediction. Past returns do not tell you what will happen next.
This tool gives an estimate for general information only. It is not financial or investment advice.