# Annualizing a Multi-year Return

It helps to compare apples-to-apples when assessing the performance of different investments. If you try to compare one investment’s five-year return with another’s two-year return, it’d be tough to see how they would match up on a given year. Annualizing a multi-year return converts it to a single-year return, which is the common figure used to compare investments. A return is the percentage you gain or lose on an investment based on its price change and income payments.

## Annualized Return Calculation

The formula to annualize a multi-year return is ((1 + R)^(1/N)) - 1. But, have no fear — there are only two figures to plug in. R represents the multi-year percentage return as a decimal and N represents the number of years of the multi-year return. For example, if an investment generated a 30 percent three-year return, the formula would be ((1 + 0.3)^(1/3)) - 1. A few calculator keystrokes gets you a result of 0.09, or a 9 percent annualized return.

## Interpretation

The annualized return is the percentage return an investment would need to have achieved annually to reach its multi-year return if its returns were the same each year. When comparing investments, the one with the higher annualized return performed better on an average year. In the previous example, if the investment earned a 9 percent return annually for three years, it would achieve a 30 percent return for the entire three-year period. This investment would have performed better on a typical year than one with an 8 percent annualized return.

## Compounding

Notice from the previous example that if you multiply a 9 percent annual return by three years, you get 27 percent, which is less than the actual 30 percent three-year return. That’s because the annualized return formula factors in compounding, which is the effect of earning returns on previously earned returns. Compounding creates a snowball effect that increases an investment’s value at a faster rate. As an investment earns a return, its value increases so that the next year’s return is calculated based on a larger investment value.

## Considerations

Although an annualized return is a handy comparison tool, an investment’s actual annual returns might have differed widely. Also, an annualized return is based on past results. The future might be completely different. Say a stock generated a 55 percent four-year return with a 12 percent annualized return. It might have taken a huge loss in the first year, but generated positive returns in later years to reach its multi-year return. Going forward, its annual returns might be a far cry from 12 percent, for better or worse.