# Annual Total Return The annual total return refers to the average return of investment each year over a certain period of time. This figure can be used to compare investments even if those investments covered different time periods. It provides a geometric average (a number that can replace each of the numbers involved so that their product does not change), not an arithmetic one.

## What Is Annual Total Return?

It is the total sum earned by an investment each year during a specific time period. Calculated as a geometric or compound average, it forecasts what an investor would earn over a given period if the annual return was compounded. The ATR gives only a snapshot of an investment's performance and does not indicate its volatility. Since the annual total return is based on past figures, it is important to remember that the future results may be quite different.

It is calculated by using this formula: [(1+R1) * (1+R2)...(1+Rn)(1/n), where R is the annual return for a given year, and n is the number of years the mutual funds have been held.

Let's suppose that you invest in two mutual funds.

• Fund 1 has been held for 2 years, with an annual return of 15%.

• Fund 2 has been held for 4 years, with an annual return of 25%.

• As a result, the ATR for Fund 1 is 7.2% whereas the figure for Fund 2 is 5.7%.

The difference between the annual and annual total returns is that the latter includes the effect of the dividends and calculates the return that you would get if you reinvested these dividends.

## Annual Total Return vs. Cumulative Return

The cumulative return indicates the aggregate effect of the price change on the investment value. To calculate the CR, use this formula:

Rc = ( Pcurrent – Pinitial ) / Pinitial

where Pcurrent and Pinitial are the current and initial prices. A cumulative return can also be negative. For example, if an investor pays \$70 for a stock that is trading at \$30 a year later, their CR is:

(\$30-\$70) / \$100 = -0.4 = (40%)

If you have a CR for a given period, even if it is a specific number of days, it is possible to calculate an annualized performance figure according to this formula:

ATR = (1 + cumulative return) (365 / days held) – 1

Let's suppose that you have held a mutual fund for 500 days and earned a CR of 24.75%. In this case, the ATR would be:

ATR = (1 + 24.75%) (365 / 500) - 1 = 117.5% - 1 = 17.5%

## ATR vs. Simple Average Return

The difference between the simple (arithmetic) and compound (geometric) averages are impacted by volatility: the higher the volatility, the greater the gap between the simple and compound averages. They can be identified only in the case of earning the same annual return for three years.

Calculations of simple averages work only when the figures do not depend on each other. The annual return is used because the amount of investment loss or gain over one year depends on the amount from other years, assuming that the annual returns are compounded.

For instance, if a manager of a mutual fund loses half of their client's money, they have to make a 100% return to reach a break-even point. More accurate ATR figures also give a clearer picture when comparing the return of stocks that have traded over various periods of time or different mutual funds.

## The Bottom Line

The ATR is the average return of investment each year over a specific period of time, which is calculated as a geometric average. This figure reflects the actual economic reality of an investment decision but does not indicate the volatility of this investment. It can be replaced by a simple average only when the figures are not interdependent.

To calculate the ATR, two key figures are used: the annual return for a given year (excluding the dividends) and the number of years the mutual funds have been held. It is also possible to use the cumulative return - aggregate effect of the price change on the investment value – for this calculation.