A +50% year, then a -50% year
The average of +50% and -50% is exactly 0% — (50 + (-50)) ÷ 2 = 0. On paper, that looks like breaking even.
What actually happened to the money
₹100 growing 50% in year one becomes ₹150. That ₹150 then falling 50% in year two becomes ₹75 — not back to ₹100. The investment actually lost a quarter of its value over the two years, even though the simple average of the two yearly returns is 0%.
What CAGR correctly shows instead
Running the real ₹100-to-₹75-over-2-years numbers through the CAGR formula gives -13.4% per year, and -25% total growth — accurately reflecting the actual loss, unlike the arithmetic average's misleading 0%.
One more connection, ROI over a single year
For a one-year holding period specifically, CAGR and simple ROI (return on investment) become the same calculation — ₹1,00,000 growing to ₹1,20,000 over exactly 1 year gives both a CAGR and a total growth figure of 20%. The gap between CAGR and simple average return only opens up once volatility and multiple compounding periods enter the picture, which a single-year ROI figure never has to deal with.
The takeaway
Whenever returns vary from period to period, arithmetic average return will equal or overstate the investment's true compounded growth rate — CAGR is always the more accurate figure for describing what actually happened to the money.