Measures return on investment from the amount invested and the amount returned, and — when you supply a holding period — the annualised rate over that period.
Simple ROI is profit divided by cost, expressed as a percentage. It says nothing about time, and that omission is what makes it easy to misread: a forty per cent return is excellent over a year and poor over a decade, and the headline figure is identical in both cases. The annualised figure, the compound annual growth rate, is the fix — it expresses the same result as an equivalent constant yearly rate, which is what makes two investments of different lengths comparable at all. If nothing came back, the annualised rate is reported as undefined rather than as minus one hundred per cent, because the compound formula has no answer there.
Comparing returns honestly
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Simple ROI ignores time:
always pair it with the holding period, or you are comparing figures that are not comparable.
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CAGR smooths out the path:
it describes the same start and end points as a constant rate. A volatile investment and a steady one with identical endpoints show the same CAGR and are not the same risk.
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Costs belong in the invested figure:
fees, commissions and taxes reduce the real return and are frequently left out of the headline number.
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Return without risk is half a picture:
a high return earned by taking a large chance of total loss is not better than a modest one earned safely, and no single percentage can show the difference.
What simple ROI leaves out entirely
Simple ROI is profit divided by cost, expressed as a percentage, and the [msm_tool slug="roi-calculator"] calculates it directly from the amount invested and the amount returned. What that headline figure says nothing about is time: a forty per cent return is an excellent result over a single year and a poor one over a decade, and the percentage itself looks identical either way, which is exactly what makes it easy to misread on its own.
CAGR is what makes different holding periods comparable
Supplying a holding period produces the annualised rate, the compound annual growth rate, which expresses the same total result as an equivalent constant yearly rate rather than one lump percentage. That is the figure that actually lets two investments held for different lengths of time be compared honestly, since simple ROI alone cannot distinguish a quick win from a slow one that happens to add up to the same total.
Why a total loss shows as undefined rather than minus one hundred per cent
The compound growth formula has no defined answer when the ending value is zero, so reporting an annualised rate for a total loss would mean inventing a number the underlying mathematics does not actually produce. Reporting it as undefined instead of forcing out a figure that looks precise but is not real preserves the honesty of the result at the cost of a slightly less satisfying answer.
Costs belong inside the invested figure
Transaction costs, management fees and any tax paid all reduce what was genuinely earned, and adding them to the amount invested — or deducting them from the amount returned — before calculating keeps the result honest. A return calculated before those costs are accounted for consistently overstates the real outcome, sometimes by a considerable margin.
A return without its risk is only half the picture
A volatile investment and a perfectly steady one can arrive at identical start and end points and therefore show an identical CAGR, despite being genuinely different propositions in every other respect. No single percentage, however carefully calculated, can show how much risk was taken to reach that number, which is why the same ROI on two different investments does not make them equivalent.