Average return of an investment
The average return tells you how fast your money grew each year on average. This average return calculator covers the two usual situations: an account with deposits and withdrawals on different dates, and a series of holding periods with known returns.
Average return based on cash flow
When you add and take out money over time, a simple percentage gain is misleading, because each dollar was invested for a different length of time. The calculator finds the yearly rate r that makes all deposits and withdrawals, on their dates, add up to the ending balance:
Sum of CFk / (1 + r)tk = 0, where CFk is each cash flow (deposits negative, withdrawals and the ending balance positive) and tk its time in years from the start.
This is the money-weighted return, also called the internal rate of return or XIRR in spreadsheets. It has no closed formula, so the calculator finds it by trial.
Example: you start with $5,600 on January 1, 2023, add $5,000 in January 2024, take out $1,500 in June 2024, add $3,800 in January 2025, and the account is worth $18,000 on December 31, 2026. The average return is 11.00% a year.
Average and cumulative return
- Cumulative return = (1 + r1)t1 × (1 + r2)t2 × … − 1, the total growth over all periods.
- Average (annualized) return = (1 + cumulative return)1 / total years − 1, the yearly rate that gives the same growth: the geometric average.
Returns of 10% a year for 1 year and 2 months, then −2% a year for 5 months, then 15% a year for 2 years and 3 months give a cumulative return of 51.78% over 3 years and 10 months, an average of 11.50% a year.
Why not the simple average?
The simple (arithmetic) average adds the yearly returns and divides by the number of years. It overstates the growth whenever returns go up and down, because a loss needs a bigger gain to recover. $10,000 invested for these 5 years:
| Year | Return | Balance |
|---|---|---|
| 1 | 20% | $12,000 |
| 2 | −10% | $10,800 |
| 3 | 15% | $12,420 |
| 4 | −5% | $11,799 |
| 5 | 10% | $12,979 |
The simple average is 6.00%, but $10,000 at 6.00% a year would grow to $13,382, not $12,979. The real average, the geometric one, is 5.35% a year. Both calculators on this page use the geometric average.
The gain needed to make up a loss
| Loss | Gain to recover |
|---|---|
| −10% | 11.11% |
| −20% | 25% |
| −30% | 42.86% |
| −50% | 100% |
−50% followed by +50% leaves you with 75% of your money. The simple average of the two returns is 0%, but the real average is −13.40% a year.
Money-weighted or time-weighted return
- Money-weighted return (the cash flow calculator): counts when and how much you invested, so it shows how your own money did.
- Time-weighted return (the average and cumulative calculator): links the returns of each period and ignores deposits and withdrawals, so it shows how the investment itself did. Funds report their returns this way.
For a single investment with a buy and a sell date, the ROI calculator gives the annualized return, and for regular cash flows the IRR calculator. To see what a return grows to over time, use the investment calculator or the compound interest calculator, and for fund fees the mutual fund calculator.