Your annualized return is the steady yearly rate that turns your starting value into your ending value. It puts investments held for different lengths of time on equal terms.
It's never higher than the plain average of your yearly returns, and it's often much lower. Returns of +50%, −30% and +10% average 10% a year, yet $10,000 grew only 4.92% a year.
From total gain to a yearly rate
The exponent is what builds in compounding. It finds the one rate that, applied each year to a growing balance, lands exactly on your ending value.
The usual shortcut divides the total gain by the years. FINRA calls that simple average an "inflated view", because it ignores compounding. Years can be a fraction, too: enter 1.5 for eighteen months.
What belongs in the start and end values?
Use totals, not share prices. FINRA's guide to investment returns starts with the full cost: the price you paid plus any fees. When you sell, take the commission off the sale proceeds.
Add any dividends you took in cash to the ending value. Reinvested dividends are already in your balance, so don't count them twice. The result is still before tax and inflation; the real rate of return calculator strips out inflation.
Why a 10% average can mean 4.92% a year
Another shortcut averages the yearly returns. It treats a loss and an equal gain as if they cancel out, but they don't. After a 30% fall, you need a gain of about 43% just to get back to even.
Each path below starts at $10,000 and averages 10% a year over three years. The wider the swings, the lower the rate you actually earned:
| Yearly returns | Value after 3 years | Annualized return |
|---|---|---|
| +10%, +10%, +10% | $13,310 | 10.00% |
| +20%, 0%, +10% | $13,200 | 9.70% |
| +30%, −10%, +10% | $12,870 | 8.77% |
| +50%, −30%, +10% | $11,550 | 4.92% |
Only the steady path earns the full 10%. The bumpiest one earns less than half of that, from the same average.
Don't annualize a few good months
Annualizing a short gain assumes the same pace for a whole year. Here's one 8% gain on $10,000, reached over different lengths of time:
| Time to gain 8% | Years to enter | Annualized return |
|---|---|---|
| 3 months | 0.25 yr | 36.05% |
| 6 months | 0.50 yr | 16.64% |
| 9 months | 0.75 yr | 10.81% |
| 1 year | 1 yr | 8.00% |
| 2 years | 2 yr | 3.92% |
Nobody earned 36.05% in the first row; they made 8% in a quarter and projected it forward. The Global Investment Performance Standards (GIPS) are globally accepted rules for how investment firms present results. They say returns for periods under one year "must not be annualized."
For a holding under a year, quote the plain gain and say how long it took.
Money added along the way breaks the formula
The calculator compares two snapshots, so it can't tell a deposit from a gain. Say you opened an account with $10,000, added $10,000 three years later, and it's worth $24,000 after five years.
| How the account is measured | Yearly rate |
|---|---|
| $10,000 at the start vs $24,000 at the end (deposit ignored) | 19.14% |
| Deposit subtracted from the end value ($10,000 vs $14,000) | 6.96% |
| Each deposit dated: year 0 and year 3 (IRR) | 5.26% |
Both shortcuts overstate what your money earned. Only the last row, at 5.26%, dates each deposit. That's the internal rate of return.
To get it for your own account, use the IRR calculator. Enter one amount per year, with zeros for quiet years. Deposits go in as negative numbers and the final value as a positive one.
Checking a fund's reported returns
Mutual fund ads can't show a flattering window on its own. Under SEC Rule 482, fund ads quoting performance must include average annual total return for one, five and ten years. Those figures must be current to the most recent calendar quarter.
So compare like with like. If a fund shows a five-year figure, run your own numbers over the same five years, with dividends included. For a quick total gain in percent instead, use the percentage return calculator.