The arithmetic mean of a series of annual returns is always at least as high as the compounded outcome an investor actually experienced - equal only when every year returns exactly the same. The gap between the two isn’t a rounding error, and it doesn’t shrink with volatility. It grows with it.
The classic case: a portfolio returns +50% one year, -50% the next. The arithmetic mean of those two numbers is 0%. What actually happened to ₹1: it becomes ₹1.50, then ₹0.75 - a 25% loss of capital, a CAGR of about -13.4%. Repeat that same two-year cycle for a decade and ₹1 becomes roughly 24 paise - a 76% cumulative loss, while the “average” return across all ten years is still exactly 0%.
Value of ₹1 compounding through an alternating +50%/-50% return cycle for ten years, against what the value would be if the 0% arithmetic average held every year.
This isn’t specific to this one toy example. There is an exact relationship: the compound growth rate is approximately the arithmetic mean minus half the variance of returns (G ≈ μ - ½σ²). It falls straight out of the mathematics of compounding, documented as “variance drain” since a 1995 paper by Tom Messmore, and it shows up in continuous time too - the same correction term appears when geometric Brownian motion is solved through Itô’s lemma. Every unit of volatility quietly costs compounded return, even when the arithmetic average printed on a factsheet hasn’t moved at all.
This is why AMFI acted. SEBI had flagged that return illustrations in mutual fund advertisements could lead investors to believe they were looking at something close to a fixed return. AMFI’s Best Practices Guidelines Circular No. 109/2023-24, dated 1 November 2023, restricted fund advertisements to CAGR - compounded annualised return - ruling out a simple average of yearly returns as the headline number. The same circular fixed exactly which figures schemes are even permitted to quote: for equity schemes, a maximum past return of 12.64% for the Sensex and 12.93% for the Nifty, based on the mean of 10-year rolling CAGRs between 1 June 2013 and 30 May 2023 - a ceiling a fund can no longer raise by switching measures.
None of this means every “average return” figure quoted before November 2023 was dishonest - a simple average is a real, if incomplete, description of a return series. It means the two numbers can legitimately differ for any volatile investment, that the difference favours whichever number is being advertised, and that since November 2023 Indian mutual fund advertising has been required, by rule rather than convention, to quote the one number that describes what an investor holding the whole period actually experienced.
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