Average Annual Return (AAR)

The average annual return (AAR) is a measure of the typical yearly return an investment has produced over a period of several years, expressed as a percentage. It is widely used to describe the performance of mutual funds, exchange-traded funds, stocks and portfolios. The figure usually includes price changes and reinvested income such as dividends and interest, making it a form of total return.

The term is used in two ways. In everyday use, AAR is often the simple arithmetic mean of yearly returns. In regulated US fund disclosures, "average annual total return" is calculated as a compound rate, the steady yearly return that would produce the same overall result, which is the same idea as an annualized return or the compound annual growth rate. Knowing which method is used is essential when comparing figures.

Imagine an investment that gains 20% one year, loses 10% the next, then gains 15% and 5%. Asked "how much did it make a year on average?", there are two honest answers. One adds up the yearly results and divides by four. The other asks what single steady yearly return would have turned your starting money into your final money.

The second answer is usually a little lower, because losses hurt more than gains help: after a 10% fall, you need an 11% rise just to get back. Fund documents in the United States use the second answer, so that investors see what actually happened to their money.

The simple (arithmetic) average annual return is:

The compound (geometric) average annual return is:

• $r_t$ is the return in year $t$, written as a decimal.
• $n$ is the number of years.

For yearly returns of 20%, −10%, 15% and 5%, the simple average is (20 − 10 + 15 + 5) ÷ 4 = 7.5%. The compound calculation multiplies 1.20 × 0.90 × 1.15 × 1.05 = 1.3041, then takes the fourth root: $1.3041^{1/4} - 1 \approx 6.86\%$. An investment of $10,000 would have grown to $13,041, which matches 6.86% a year compounded, not 7.5%.

US mutual fund rules require prospectuses and advertisements to show average annual total returns for standard periods, typically one, five and ten years or since launch, calculated on a compound basis after deducting fees and, where applicable, maximum sales charges. Funds also show after-tax returns in some documents and compare results with a benchmark index. Similar standardised reporting exists in other markets, such as the EU's key information documents. Standardisation lets investors compare funds on the same basis, while the expense ratio shows how much of the gross return goes to costs.

A single average says nothing about how bumpy the ride was. Two funds can both show a 7% AAR, one with steady results and one with large swings. Investors therefore look at the standard deviation of returns, the largest peak-to-trough fall and ratios such as the Sharpe ratio to judge risk-adjusted return. Rating services such as the Morningstar rating combine return and risk into a single score for this reason.

Crypto assets often show extremely high arithmetic average returns because of a few spectacular years, while their compound returns are lower because of deep crashes in between. Short histories, survivorship and the choice of start date can make crypto AAR figures misleading. Many tokens that once showed huge averages have since lost most of their value, which highlights why compound figures and drawdowns matter more than headline averages.

AAR depends heavily on the period chosen; starting just after a crash flatters results, while ending just after one depresses them. Past averages do not predict future returns. Fund averages can suffer from survivorship bias when closed funds drop out of comparisons. Nominal AAR also includes inflation, so real returns can be much lower in periods of rising prices.