annualized

Annualized is a term used to describe converting a rate, return, or metric measured over a shorter or irregular interval into a value on an annual basis. It is commonly used in finance to compare performance or risk across instruments and time periods, but the concept appears in statistics and other fields as well.

In finance, the most common forms are annualized returns and annualized volatility. If a return r is observed over a period with m equal intervals per year, the annualized (effective) return is (1 + r)^m − 1. For variable periodic returns, the general approach uses a geometric average: the product of (1 + r_i) across observed periods, raised to the power m divided by the number of periods, minus 1. The continuously compounded annualized return can be expressed as m × ln(1 + r) or equivalently ln((1 + r)^m). Annualized volatility scales with the square root of time: if sigma is the period standard deviation and there are m periods per year, the annualized sigma is sigma × sqrt(m).

Common applications include reporting investment performance over standard horizons (1-, 3-, 5-, 10-year annualized returns) and comparing risk (volatility) across assets. It is also used to project future values from short-term observations.

Limitations include the assumption of consistent conditions, which may not hold in practice, and potential misinterpretation when data exhibit seasonality or non-stationarity. Annualization can exaggerate or understate true performance if the underlying period is not representative. It is important to specify the method and the underlying data when presenting or interpreting annualized figures.