CAGR against absolute return, and why the gap matters
How a smoothed annual rate is calculated, why it is the only fair way to compare investments of different lengths, and the three things it deliberately hides.
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In short
- CAGR is the constant annual rate that would take the starting value to the ending value. It is not the average of the yearly returns.
- An absolute return of 50% is 14.47% a year over three years and 6.99% a year over six. The same gain, very different investments.
- It hides volatility completely. Two investments with the same CAGR can have had entirely different journeys and different risks.
- It cannot handle money added or withdrawn along the way. For a SIP or any irregular cash flow, XIRR is the correct measure.
- The arithmetic mean of yearly returns always overstates the real one. Only the geometric mean, which is what CAGR computes, matches the money.
Compound annual growth rate answers a single question: at what constant annual rate would this investment have had to grow to get from where it started to where it ended?
CAGR = (final ÷ initial)^(1 ÷ years) − 1
It is the smoothed rate, and smoothing is both its usefulness and its limitation.
Why absolute return is not enough
An investment that grows from ₹1,00,000 to ₹3,00,000 has returned 200%. That figure is true and almost useless on its own, because it says nothing about how long it took.
| Gain | Over 3 years | Over 6 years | Over 10 years |
|---|---|---|---|
| 50% | 14.47% a year | 6.99% a year | 4.14% a year |
| 100% | 25.99% | 12.25% | 7.18% |
| 200% | 44.22% | 20.09% | 11.61% |
The row for 50% is the clearest illustration. Doubled over six years rather than three, an identical gain becomes a mediocre one — 6.99% is below what a fixed deposit pays.
Absolute return is what happened. CAGR is the rate at which it happened, and only the rate can be compared across investments held for different lengths of time.
It is not the average of the yearly returns
This is the part people get wrong, and it is worth being precise about.
Take an investment that gains 50% in year one and loses 50% in year two. The arithmetic mean of those returns is zero. The money is down 25%: ₹100 becomes ₹150, then ₹75.
CAGR gets this right, because it works from the starting and ending values rather than from the returns. (75 ÷ 100)^(1/2) − 1 = −13.4%. Compounding −13.4% twice gives exactly the −25% observed.
The arithmetic mean always overstates, and the gap grows with volatility:
| Year 1 | Year 2 | Arithmetic mean | True CAGR |
|---|---|---|---|
| +10% | −10% | 0% | −0.50% |
| +30% | −30% | 0% | −4.61% |
| +50% | −50% | 0% | −13.40% |
| +100% | −100% | 0% | −100% |
The last row is the extreme case and the reason it matters: a 100% loss cannot be recovered by any subsequent gain, and no arithmetic mean will tell you that.
This is why fund factsheets quote CAGR rather than average annual return, and why any promotional material quoting the arithmetic mean of yearly returns is presenting a better number than the investor actually received.
What CAGR hides
Volatility, entirely. Two investments both showing 12% CAGR over ten years may have been utterly different experiences: one rising steadily, the other doubling, halving and doubling again. CAGR sees only the endpoints. For risk you need standard deviation, maximum drawdown, or simply the year-by-year figures.
The path, which affects real behaviour. An investment that fell 60% in its third year has a 12% CAGR only for the investor who did not sell. Most did.
Everything in between. If the ending date happens to fall just after a market peak, the CAGR flatters; just after a crash, it damns. This is why fund comparisons use rolling returns — CAGR computed across many overlapping periods — rather than one convenient window. A fund advertising "18% CAGR" from a start date of March 2020 has chosen the bottom of a crash as its zero.
Cash flows. CAGR assumes one amount in at the start and one out at the end. Add money in the middle and it is simply the wrong tool.
For a SIP, use XIRR
A systematic investment plan puts money in on many dates. Each instalment has its own holding period, so there is no single "initial value" for CAGR to work from.
The correct measure is XIRR, the internal rate of return over irregular cash flows: the annual rate that makes the present value of everything you paid in equal to what you ended with. Every spreadsheet has the function, and every fund statement reports it.
Applying CAGR to a SIP by treating total invested as the initial value produces a badly wrong answer — always too low, because it assumes all the money was in from day one when the last instalment was in for a month.
The same applies to any portfolio you have added to. CAGR describes a single lump sum, left alone.
Reading a CAGR honestly
Three questions make almost any quoted CAGR interpretable.
Over what period? A CAGR over three years says little about a strategy; over fifteen it says a great deal. Short periods are dominated by where the market happened to be at each end.
Starting when? Ask what the same number looks like starting a year earlier and a year later. If it moves dramatically, the number is describing the market's timing rather than the investment's quality.
Against what? 14% CAGR is excellent against a benchmark that returned 9% and unremarkable against one that returned 16%. An equity fund's CAGR without its index alongside it is half a sentence.
Using it to work backwards
The formula rearranges usefully. To find what a target implies:
required CAGR = (target ÷ current)^(1 ÷ years) − 1
Turning ₹10 lakh into ₹50 lakh in ten years needs 17.46% a year — well above what Indian equity has delivered over most long periods, which tells you the plan needs either more time, more contributions, or a smaller target. Better to discover that now than in year nine.
Run in the other direction, the same formula converts any promise into a rate. A scheme offering to triple money in four years is claiming 31.6% a year, which is a claim to beat every professional fund in the country, sustained, with no bad years.
Rolling returns, and the date the marketing chose
A single CAGR depends entirely on two dates, and whoever prepared the number chose them.
Rolling returns fix this. Rather than one ten-year window, compute the ten-year CAGR starting from every month in the fund's history and look at the distribution: the best, the worst, the median, and how often it beat its benchmark. A fund whose worst ten-year rolling return is 9% is a different proposition from one whose worst is −2%, even if both average 13%.
This is the single most useful discipline available to a retail investor comparing funds, and it costs nothing — most Indian fund research sites publish rolling return charts.
The related habit is to check what a number looks like from a neighbouring start date. Any figure that changes by more than a few points when the start moves a year is describing the market's timing rather than the manager's skill.
Comparing across asset classes
CAGR makes very different investments comparable, provided the inputs are consistent.
Property returns quoted as CAGR usually omit stamp duty, registration, brokerage, maintenance and property tax, all of which are real and none of which appear in the purchase and sale prices. Gold returns rarely account for making charges or storage. Fund returns are net of the expense ratio but gross of tax, and the tax treatment differs sharply between equity, debt and property.
Put every asset on the same footing — net of costs, net of tax, over the same period — before ranking them. Most comparisons that reach a surprising conclusion have simply put one asset on a different footing from the other.
What this calculator assumes
- One amount invested at the start and one value at the end, with nothing added or withdrawn in between.
- The period is measured in years and may be fractional.
- The result is a smoothed rate; it does not describe the path taken or the risk involved.
- Figures are before tax and before charges. Both reduce the CAGR you actually keep.
- A negative CAGR is reported as such rather than suppressed, because a loss expressed as an annual rate is the honest comparison.