What is an annualized return (CAGR)?

An annualized return is the constant yearly rate that would turn the starting value into the final value over the same number of years. It is also called the compound annual growth rate (CAGR). It makes returns over periods of different length comparable: 50% over five years and 20% over two years can only be put side by side once both are expressed per year.

The formula

\text{CAGR} = \left(\frac{V_{\text{end}}}{V_{\text{start}}}\right)^{1/n} - 1

where $V_{\text{start}}$ and $V_{\text{end}}$ are the values at the start and at the end, and $n$ is the number of years. It need not be a whole number: 30 months is $n = 2.5$ .

If the total return $R$ over the period is already known, the same formula reads:

\text{CAGR} = (1 + R)^{1/n} - 1

A simple illustration

An investment grows from €10,000 to €16,105 in five years, a total return of 61.05%.

\text{CAGR} = \left(\frac{16{,}105}{10{,}000}\right)^{1/5} - 1 = 10\%

Growing by exactly 10% every year for five years produces the same result. Note that 61.05% divided by five is 12.2%, which overstates the yearly rate: each year's gain also earns returns in the following years.

Why it is not the average of the yearly returns

An investment gains 50% in the first year and loses 50% in the second. The average of the two yearly returns is 0%, but the investment is not back where it started:

10{,}000 \times 1.5 \times 0.5 = 7{,}500

The annualized return is:

\left(\frac{7{,}500}{10{,}000}\right)^{1/2} - 1 \approx -13.4\% \text{ per year}

The arithmetic average overstates what was earned whenever returns vary from year to year, and the more they vary, the larger the gap. This is one reason volatility costs money even when the average return looks the same. The annualized return is the geometric average, and it is the one that describes what actually happened to the money.

Things to keep in mind

Short periods mislead. Annualizing a 5% gain over two months gives about 34% a year, which says very little about the other ten months. Most performance reports only annualize periods longer than a year.
Cash flows need care. For a portfolio with deposits and withdrawals, the start and end values alone do not work: annualize the time-weighted return instead, or use the money-weighted return, which is already a yearly rate.
It hides the path. Two investments with the same annualized return can have gone through very different drawdowns on the way.

See these numbers for your own portfolio

Floreo works out every figure on this page from your own holdings — returns, risk, allocation, currencies — and the assistant explains them the way this page does. Import from your broker, or try it on the sample portfolio first.

Start Demo

The demo opens straight away on a sample portfolio — no account needed.