# Annualized Rate

## What is an 'Annualized Rate'

An annualized rate of return is calculated as the equivalent annual return an investor receives over a given period of time. The Global Investment Performance Standards dictate that returns of portfolios or composites for periods of less than one year may not be annualized. This prevents "projected" performance in the remainder of the year from occurring.

## BREAKING DOWN 'Annualized Rate'

Annualized returns are returns over a period of time scaled down to a 12-month period. This scaling process allows investors to objectively compare the returns of any assets over any periods of time.

## Calculation Using Annual Data

Calculating the annualized performance of an investment or index using yearly data utilizes the following data points:

P = principal, or initial investment

G = gains or losses

n = number of years

AP = annualized performance rate

The generalized formula, which is exponential to take into account compound interest over time, is:

AP = ((P + G) / P) ^ (1 / n) - 1

For example, assume an investor invested \$50,000 into a mutual fund, and four years later, the investment is worth \$75,000. This is a \$25,000 gain 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 approximately 10.67%.

A \$25,000 gain on a \$50,000 investment over four years is a 50% return. It is inaccurate to say the annualized return is 12.5%, or 50% divided by four, because this does not take into effect compound interest. If reversing the 10.67% result to compound over four years, the result is exactly what is expected:

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

It is very important not to confuse annualized performance with annual performance. The annualized performance is the rate at which an investment grows each year over the period of time to end up at the final valuation. In this example, a 10.67% return each year for four years turns \$50,000 into \$75,000. But this says nothing about the actual annual returns over the four-year period. Returns of 4.5%, 13.1%, 18.95% and 6.7% turn \$50,000 into approximately \$75,000. Also, returns of 15%, -7.5%, 28% and 10.2% provide the same result.

## Using Days in the Calculation

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

AP = ((P + G) / P) ^ (365 / n) - 1

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

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

The annualized performance in this example is 12.31%.