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CAGR Explained: The Formula Behind "Annualized Return"

CAGR answers one specific question: if your investment had grown at a perfectly steady rate every year, what would that rate have been? Here is the formula and why it matters.

The formula: (Ending Value / Beginning Value)^(1/years) - 1

Take the ratio of what you ended with to what you started with, raise it to the power of 1 divided by the number of years, then subtract 1. The result, as a percentage, is the CAGR.

It smooths out year-to-year volatility into one number

CAGR does not care whether the path from start to end was a smooth climb or a wild rollercoaster β€” it only looks at the starting value, ending value, and the number of years between them.

It is not the same as averaging yearly returns

A simple average of, say, +50% one year and -50% the next gives 0%, but the actual result is a 25% loss overall (1.5 Γ— 0.5 - 1). CAGR reflects this compounding effect correctly, while a simple average does not.

Its main use is comparing investments over different time periods

CAGR lets you compare a 3-year investment and a 7-year investment on the same "per year" basis, which a raw total-return percentage cannot do fairly.

A worked example

Start with $10,000, end with $16,000 after 5 years: CAGR = (16000/10000)^(1/5) - 1 = 1.6^0.2 - 1 β‰ˆ 9.86%. This does not mean the investment grew by exactly 9.86% every single year β€” some years may have been up 30%, others down 10% β€” it means a hypothetical steady 9.86% annual growth rate would have produced the same overall result.

Why CAGR can be misleading on its own

Because CAGR only uses the start and end points, it completely ignores the volatility and drawdowns experienced in between. Two investments with the identical CAGR can have had wildly different risk profiles along the way, one steady and one that dropped sharply before recovering, so CAGR should be read alongside a volatility or risk measure, not as a complete picture of an investment's quality by itself.

Frequently Asked Questions

Is CAGR the same as "annualized return" or "average annual return" you see quoted in ads?

"CAGR" and "annualized return" generally refer to the same compounding-based calculation. "Average annual return," if it means a simple arithmetic average of yearly returns, is a different and usually more misleading number, since it overstates results for volatile investments, as shown by the +50%/-50% example.

Can CAGR be negative?

Yes β€” if the ending value is lower than the beginning value, the formula produces a negative percentage, correctly reflecting an overall loss annualized over the period.