Annualized Total Return

What it is

Annualized total return (also called compound annual growth rate or CAGR) is the geometric average annual rate of return earned by an investment over a specified period. It shows the constant annual rate at which an investment would have grown if returns were compounded each year. It does not measure volatility or the year‑to‑year ups and downs of the investment.

Key takeaways

• Annualized total return is a geometric (compound) average, so it accounts for compounding.
• It answers: “What constant annual return would produce the observed cumulative result?”
• Use the geometric formula for multi‑period returns and a time‑adjusted formula when converting a cumulative return over days to an annual figure.
• Annualized return is usually lower than the arithmetic average of period returns when returns vary across periods.

How to calculate

For n periods with periodic returns r1, r2, …, rn (each expressed as decimals, e.g., 5% = 0.05):

Annualized Return = (Π (1 + ri))^(1/n) − 1

Example (five years)
* Returns: 3%, 7%, 5%, 12%, 1%
* Multiply growth factors: (1.03)(1.07)(1.05)(1.12)(1.01) = 1.30913 (approximately)
* Fifth root: 1.30913^(1/5) ≈ 1.0553
* Annualized return ≈ 1.0553 − 1 = 0.0553 → 5.53%

Converting a cumulative return over days to an annual rate

When you have a cumulative return over a specific number of days:

Annualized Return = (1 + Cumulative Return)^(365 / Days Held) − 1

Example
* 575 days, cumulative return = 23.74% → (1.2374)^(365/575) − 1 ≈ 14.5% annualized

Annualized return vs. average (arithmetic) return

• Arithmetic average = (r1 + r2 + … + rn) / n. It ignores compounding and can overstate typical annual growth when returns fluctuate.
• Annualized (geometric) average incorporates compounding: it reflects the real growth rate of an investment over time and is the preferred metric for multi‑period performance.

Reporting considerations

Industry standards (for example, the Global Investment Performance Standards, GIPS) generally require at least 365 days of track record before reporting an annualized return. Shorter periods should be reported as cumulative past performance rather than extrapolated annual figures.

Common questions

What does a “3‑year annualized return” mean?
* It is the geometric average annual return over a three‑year period — the constant yearly growth rate that compounds to the observed three‑year result.

Is a 10% annualized return good?
* “Good” depends on objectives, risk tolerance, time horizon, and the relevant benchmark. Historically, broad U.S. stock market returns have averaged around this level over long periods, but individual goals and risk profiles determine whether 10% is desirable.

Bottom line

Annualized total return (CAGR) provides a clear, compounding‑adjusted picture of how an investment performed on an annual basis over a multi‑period horizon. It’s useful for comparing investments and understanding growth over time, but it does not show volatility or sequence of returns — metrics you should also consider when evaluating investments.