ROI and CAGR: what the two measures mean, and where they mislead

Compound annual growth rate is the answer to ROI's silence about time. It asks a different question: what steady annual rate of growth would have taken the initial value to the final value over the same number of years? The arithmetic is a geometric mean rather than a simple division. Divide the final value by the initial value to get the total growth factor, take the nth root of that factor, where n is the number of years, and subtract one.

Work through a real example. Bitcoin opened 2016 at $430 and closed 2025 at $87,508.83. That is a growth factor of about 203.5 over nine years. The ninth root of 203.5 is approximately 1.805, so the compound annual growth rate is about 80.5 per cent per year. The claim that follows — "Bitcoin compounded at 80.5 per cent a year from 2016 to 2025" — is arithmetically correct. It is also, as the next section explains, deeply misleading if read as a description of what a holder experienced.

CAGR is the standard measure for comparing investments of different durations, and it is the figure that appears in fund factsheets and performance tables. Its virtue is comparability: a three-year CAGR and a ten-year CAGR are expressed in the same units, so they can be placed side by side. Its vice is that it assumes a smooth exponential path, and almost nothing in markets follows one.

The distinction that explains most of the confusion around annualised returns is the one between the arithmetic mean and the geometric mean. The arithmetic mean is what most people think of when they say "average": add the numbers up and divide by how many there are. The geometric mean multiplies the numbers together and takes the nth root. For a series of returns, the geometric mean is the one that corresponds to actual compounded wealth, and the arithmetic mean is the one that corresponds to nothing in particular.

The gap between them is not a rounding error. Take two years: the first returns plus 100 per cent, the second returns minus 50 per cent. The arithmetic mean is plus 25 per cent per year, which suggests a profitable investment. The geometric mean is zero, because a dollar that doubles and then halves is a dollar. The arithmetic average describes a portfolio that does not exist; the geometric average describes the one the investor actually holds.

Bitcoin's annual returns make this gap unusually wide, because the series contains both very large gains and very large losses. The arithmetic mean of the sixteen calendar-year changes in the yearly returns table is far higher than the geometric mean over the same period. Anyone who quotes the arithmetic average as though it were a growth rate is overstating the asset's performance, usually without intending to. The rule to carry away is simple: for compounding, use the geometric mean, which is what CAGR is.

A compound annual growth rate is a single number that describes the relationship between two endpoints. It contains no information about what happened in between. 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 investor's life is not.

Bitcoin is the clearest possible illustration of this. The 80.5 per cent CAGR from 2016 to 2025 is real, but 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.

This matters most for position sizing and for time horizon. An investor who reads "80.5 per cent per year" and concludes that a one-year holding period is likely to produce a similar result has misunderstood the statistic. The risk and volatility page quantifies the dispersion that the annualised figure conceals, and the drawdown record shows how deep and how long the interruptions have been. Together they are the necessary counterweight to any single annualised number.

The first example is the one most often quoted. An investor buys one bitcoin on 1 January 2017 at the year's opening price of $963 and sells on 31 December 2025 at the closing price of $87,508.83. The total return is $87,508.83 minus $963, which is $86,545.83, divided by $963, giving 89.9, or a 8,987 per cent ROI. Over nine years, the growth factor is 90.9, and the ninth root of 90.9 is about 1.65, so the CAGR is roughly 65 per cent per year. Both figures are correct, and both are almost useless without the intervening history: the same investor would have been down 61 per cent at the end of 2018 and down 64 per cent at the end of 2022.

The second example shows how sensitive the answer is to the entry point. An investor buys one bitcoin on 1 January 2021 at $29,000 and sells on 31 December 2022 at $16,520. The total return is negative: $16,520 minus $29,000 is minus $12,480, divided by $29,000, giving minus 0.43, or a 43 per cent loss. The CAGR over those two years is minus 24.5 per cent per year. This investor held through the same period as the first, in the same asset, and lost money. The difference is entirely the window. This is why the dollar-cost averaging page exists: spreading entries across time is the practical response to the fact that a single entry date can dominate the outcome.

Neither example is a recommendation, and neither is a forecast. They are arithmetic performed on published prices, included so that the reader can see exactly how the two measures behave and where each one stops being informative. The figures come from the same series published on the yearly returns page, and the source and vintage are labelled there and here.

Use ROI when the question is about a single completed transaction and the holding period is short or irrelevant. Use CAGR when the question is about comparing investments of different durations, and when you understand that it is a summary of endpoints rather than a description of the journey. Use neither when the question is about risk, because neither measure contains any information about volatility, drawdown or the probability of being forced to sell at the wrong moment.

For a volatile asset, the honest presentation of performance 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 across its returns and risk sections, and the methodology behind every number is documented on the data sources page. A reader who takes one figure away from this page should take the geometric mean, and should take it with the drawdown beside it.