Average Return Calculator

The arithmetic average is the simple sum of all returns divided by the number of periods. The geometric average accounts for compounding effects over time. For example, if you make 100% in year one and lose 50% in year two, your arithmetic average is +25%, but you are back to your starting amount, meaning your geometric (actual) return is 0%.

Geometric returns are pulled down by investment volatility. The larger the ups and downs in your portfolio, the wider the gap between your arithmetic and geometric average returns. This is often referred to as 'volatility drag'.

You should always use the geometric average return when evaluating the actual historical growth rate of an investment over multiple compounding periods. Arithmetic returns are only useful for estimating performance in a single future period.

Yes. The Compound Annual Growth Rate (CAGR) is the geometric average return of an investment over a multi-year period. It represents the smooth, annualized rate of return that would have grown the initial capital to the final sum.

If an investment loses 100% of its value (a return of -100%), the total value drops to zero. Because you cannot compound from zero, the geometric return is mathematically -100%. Losses greater than 100% are not mathematically valid for standard geometric return formulas.