Annualized Return

Annualized return is the constant yearly rate of return that would turn an investment's starting value into its ending value over a given period, with gains compounded each year. It converts a return earned over months or many years into a per-year figure, so that investments held for different lengths of time can be compared on the same footing. Fund companies, advisers and index providers publish it as a standard performance measure.

Annualized return is a geometric average, not a simple one. For a single investment with no money added or withdrawn it is the same figure as the compound annual growth rate (CAGR); the term "annualized" is more common in fund reporting, where it is applied to total return. In the United States, fund prospectuses report it as "average annual total return".

Imagine a long car journey that took you 400 kilometres in five hours. Some stretches were fast motorway and some were traffic jams, but you can still say you averaged 80 kilometres an hour. That single speed tells you nothing about the jams, yet it lets you compare this trip with another one of a different length.

Annualized return does the same for money. An investment may have jumped one year and slumped the next, but annualizing finds the one steady yearly growth rate that would have produced the same end result. Because money grows on money already gained, the calculation multiplies the yearly results together rather than simply adding them up and dividing.

Given a cumulative total return over $n$ years, the annualized return is:

• $R_a$ is the annualized return, as a decimal.
• $R_{\text{total}}$ is the cumulative total return for the whole period, as a decimal.
• $n$ is the length of the period in years, which can be fractional (for example 2.5).

If a fund gained 50% in total over four years, $R_a = 1.5^{0.25} - 1 \approx 1.1067 - 1 = 0.1067$, or about 10.67% a year. A simple division (50% ÷ 4 = 12.5%) would overstate the yearly rate, because it ignores compounding.

When the yearly returns are known, the same result comes from multiplying the growth factors: $R_a = \left[(1+r_1)(1+r_2)\cdots(1+r_n)\right]^{\frac{1}{n}} - 1$, where $r_1$ to $r_n$ are the individual yearly returns.

Take an investment that rises 50% in year one and falls 50% in year two. The arithmetic average of the two yearly returns is 0%, suggesting the investor broke even. In fact $100 became $150 and then $75, a 25% loss. The annualized return is $\sqrt{0.75} - 1 \approx -13.4\%$ a year, which correctly describes what happened. The gap between the arithmetic and geometric averages widens as volatility rises, which is why annualized figures are preferred for performance and arithmetic averages are reserved for statistical work such as estimating standard deviation.

• Fund disclosure. SEC rules require a US mutual fund to show average annual total returns for one, five and ten years, compared with a benchmark index. The UK and EU require past performance in a fund's key information documents under their own rules.
• Comparing asset classes. Long-run returns of stocks, bonds and cash are almost always quoted annualized, often alongside inflation to give a real figure.
• Planning. Advisers use an assumed annualized return to project how savings grow under compound interest, for example when sizing a retirement pot or an IRA contribution plan.
• Interest-bearing products. For deposits and loans the annualized convention appears as the annual percentage yield (APY), which includes compounding, unlike the simple annual percentage rate (APR).

A fund's published annualized return is time-weighted: it measures how each dollar in the fund performed, ignoring when investors put money in or took it out. An individual's own result is better captured by a money-weighted return (the internal rate of return), which gives more weight to periods when more money was invested. An investor who bought heavily near a peak can earn a lower money-weighted return than the fund's time-weighted figure. Both are then annualized in the same way.

An annualized return hides the path. Two investments with the same 7% annualized return can have had very different worst years and drawdowns, which is why it is read together with risk measures such as the Sharpe ratio or beta. It depends heavily on the start and end dates chosen. Annualizing a short period magnifies it: a 5% gain in one month becomes roughly 80% annualized, a figure that says little about any real year. For that reason the Global Investment Performance Standards (GIPS) do not allow returns for periods of less than a year to be annualized. Finally, it is backward-looking and does not predict future returns, a point echoed in every fund's standard disclaimer and in the risk–return trade-off any projection must respect. It is also distinct from year-to-date (YTD) figures, which are cumulative and never annualized.

• Investor.gov: Annual return
• Investor.gov: Compound interest calculator