# Annualized Rate of Return

### What is an annualized rate?

An annualized rate of return is calculated as the equivalent annual return that an investor receives over a given period. Global investment performance standards state that returns on portfolios or composites for periods of less than one year cannot be annualized. This prevents the “projected” performance for the rest of the year from occurring.

### Understanding the annualized rate

Annualized returns are returns over a period reduced to a period of 12 months. This scaling process allows investors to objectively compare the returns of all assets over any period.

### Calculation using annual data

The calculation of the annualized performance of an investment or an index using annual data uses the following data points:

P = principal or initial investment

G = gains or losses

n = number of years

AP = annualized performance rate

The general formula, which is exponential to account for compound interest over time, is as follows:

AP = ((P + G) / P) ^ (1 / n) – 1

For example, suppose an investor has invested \$ 50,000 in a mutual fund and, four years later, the investment is worth \$ 75,000. This is a gain of \$ 25,000 in four years. Thus, the annualized performance is:

AP = ((\$ 50,000 + \$ 25,000) / \$ 50,000) ^ (1/4) – 1

In this example, the annualized performance is 10.67%.

A gain of \$ 25,000 on an investment of \$ 50,000 over four years represents a return of 50%. It is incorrect to say that the annualized return is 12.5%, or 50% divided by four, because this does not take into account compound interest. If we reverse the result of 10.67% for the compound over four years, the result is exactly what is expected:

\$ 75,000 = \$ 50,000 x (1 + 10.67%) ^ 4

It is important not to confuse annualized performance with annual performance. Annualized performance is the rate at which an investment grows each year over the period to arrive at the final valuation. In this example, a 10.67% return each year for four years increases from \$ 50,000 to \$ 75,000. But that says nothing about actual annual returns over the four-year period. Returns of 4.5%, 13.1%, 18.95% and 6.7% increase from \$ 50,000 to approximately \$ 75,000. In addition, yields of 15%, -7.5%, 28% and 10.2% provide the same result.

### Use of days in the calculation

Industry standards for most investments dictate the most accurate form of annualized return calculation, which uses days instead of years. The formula is the same, except for the exhibitor:

AP = ((P + G) / P) ^ (365 / n) – 1

Assume from the previous example that the fund returned \$ 25,000 over a period of 1,275 days. The annualized return is then:

AP = ((\$ 50,000 + \$ 25,000) / \$ 50,000) ^ (365/1275) – 1

The annualized performance in this example is 12.31%.