Compound annual growth rate, explained

Total return, or return on investment, is the simpler measure: the change in value over a holding period expressed as a percentage of what was put in. It requires no annualisation and no assumption about compounding. If a position is opened at one price and closed at another, total return is the difference divided by the entry price. It is the right measure when the question is how much a position made, and it is silent about how long the money was committed.

The two measures are related but not interchangeable, and the relationship is the source of most of the confusion around them. A total return of 300 per cent earned over two years and the same total return earned over ten years are identical as total returns and very different as annual rates. CAGR converts the first into a rate of about 90 per cent a year and the second into about 15 per cent a year. Neither figure is more correct than the other; they answer different questions, and a reader who quotes one while meaning the other will mislead without intending to.

The practical rule is to use total return when comparing outcomes and CAGR when comparing rates. A reader who wants to know what a purchase produced should look at the total return. A reader who wants to know whether that outcome was good relative to the time it took should look at the annualised figure. The ROI and CAGR page works through both measures with the same published figures.

A compound annual growth rate contains no information about what happened between the endpoints. Two investments can share an identical CAGR and offer completely different experiences: one grinding upward at a steady rate, the other collapsing by eighty per cent and then recovering to the same endpoint. The number is the same. The holder's experience is not, and the difference matters for anyone who might need their money before the period ends.

Bitcoin is the clearest illustration available. The 80.5 per cent CAGR from 2016 to 2025 is real, and no year in that period actually returned 80.5 per cent. The years returned plus 124 per cent, plus 1,366 per cent, minus 73 per cent, plus 92 per cent, plus 303 per cent, plus 59 per cent, minus 64 per cent, plus 156 per cent, plus 121 per cent and minus 6 per cent. The annualised figure is a mathematical summary of those ten numbers, not a description of any one of them. A holder who needed their money in 2018 or 2022 did not receive the CAGR; they received the year.

There is a second limitation that is less often discussed. CAGR assumes the growth compounded continuously at a constant rate, which is a model rather than an observation. For an asset whose returns are as dispersed as Bitcoin's, the geometric mean is a poor description of any actual period, and the gap between the geometric and arithmetic means is unusually wide. A reader who quotes the arithmetic average of Bitcoin's annual returns as though it were a growth rate is overstating the asset's performance, usually without intending to.

The honest presentation of performance for a volatile asset is always a set of figures rather than a single one: the total return, the annualised return, the largest drawdown within the period, and the length of time the position spent below its previous peak. This site publishes all four. The drawdown record supplies the third and fourth, and the holding-period returns page shows how the annualised figure varies with the window chosen.