How the result is calculated
Return on investment answers one question: for every unit of money an investment cost you, how much came back on top? You need two totals to answer it. The first is everything the investment gave you: the price you sold it for, or what it is worth today if you still hold it, plus any income it paid out on the way, such as dividends from a share, interest from a bond or rent from a property. The second is everything it cost you: the purchase price plus the fees you paid to buy, hold and sell it. The gain is the first total minus the second, and the ROI is that gain as a share of the cost.
ROI(R − C) ÷ C
- R
- the total returned: the sale price or current value plus income received
- C
- the total cost: the amount invested plus costs and fees
That figure has a blind spot: time. A 50% gain is excellent if it took two years and poor if it took twenty. To compare the two, the calculator converts the total into an annualised return, the constant yearly rate that, compounded over the years held, would turn the cost into the same total. It is the same formula as a compound annual growth rate, and the same calculation a spreadsheet's RRI function performs.
annualised return(R ÷ C)1 ÷ t − 1
- t
- the years the investment was held, fractions allowed
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Total returned, R | $15,000.00 | Amount returned, no income |
| Total cost, C | $10,000.00 | Amount invested, no costs |
| Gain | $5,000.00 | 15,000 − 10,000 |
| ROI | 50.00% | 5,000 ÷ 10,000 |
| Growth factor, R ÷ C | 1.5 | 15,000 ÷ 10,000 |
| Annualised return | 8.45% | 1.51 ÷ 5 − 1 |
| Check | 1.0845^5 = 1.50 | the yearly rate compounds back to the total |
Dividing the 50% by five years would suggest 10% a year, but 10% compounded for five years is 61%, not 50%. The honest yearly figure is 8.45%.
| Item | Amount | How it is obtained |
|---|---|---|
| Total returned, R | $24,500.00 | 23,000 sale + 1,500 dividends |
| Total cost, C | $20,200.00 | 20,000 + 200 commission |
| Gain | $4,300.00 | 24,500 − 20,200 |
| ROI | 21.29% | 4,300 ÷ 20,200 |
| Annualised return | 6.64% | (24,500 ÷ 20,200)1 ÷ 3 − 1 |
Leave the dividends out and the ROI falls to 13.86%; leave the commission out and it rises to 22.50%. Both omissions are common, and each moves the answer by more than the commission itself suggests.
Reading the result
The headline is the ROI as a percentage of everything the investment cost. Beneath it, the net gain is the same result in money, the annualised return spreads it over the years you held the investment, and the money multiple says how many units came back for each one paid: 1.5x means half as much again.
The table under the result restates your ROI as a yearly rate for several holding periods. It is the quickest way to see why a total return on its own is not enough. The same 50% is 50% a year if it took one year, 14.5% a year over three, 4.1% over ten and 2.0% over twenty. When someone quotes an ROI without saying how long the money was tied up, that table is the question to ask.
What changes the result
The holding period changes the annualised figure, not the ROI. Every extra year spreads the same gain more thinly, so an investment you are still holding becomes a worse yearly performer each year its value stands still, even though its ROI has not moved.
Income received raises the return for anything that pays out. For a rental property or a dividend share it can be most of the return, and an ROI computed on prices alone describes a different investment from the one you owned.
Costs work the other way and are easy to underestimate. Commission on buying and selling, an annual platform charge, a fund's ongoing charge if it was taken out of your account rather than the fund's price, legal fees on a property: each one raises the cost the gain is measured against.
A loss is handled the same way. Sell for 8,000 what cost 10,000 and the ROI is minus 20%; over two years that is minus 10.6% a year, because the shortfall compounds too.
What is not included
The calculator is pre-tax. Tax on dividends, interest and gains depends on your country, your income and the account the investment sat in, and it can take a large share of the gain. To see an after-tax ROI, enter the income and the sale proceeds after the tax you paid on them.
It is also nominal. A gain of 3% a year while prices rose 3% a year left you with the same buying power you started with. The inflation calculator converts an amount between years if you want the real figure.
It assumes one purchase and one sale. If you invested more part way through, or took money out, a simple ROI weighs every unit as if it had been invested for the whole period. Fund managers use time-weighted returns for that reason, and an internal rate of return over every dated cash flow gives a money-weighted answer for your own account.
Finally, ROI says nothing about risk. Two investments with the same annualised return may have taken very different paths to it, and a return that came with a real chance of losing half the money is not the same achievement as one that never could.
Using the result
Use the annualised return, not the ROI, whenever you compare investments held for different lengths of time, and compare it with a realistic alternative for the same years: what a deposit account, a government bond or a broad index fund returned over that period. If your investment did no better than the safe alternative, the extra risk earned nothing.
Count every cost and every payout, because the gap between a careless ROI and an honest one is usually larger than people expect. And for an investment you still hold, remember that the figure is provisional: it describes a sale you have not made, at a price you have not been offered.