Annualizing

Annualizing is the process of expressing a rate, return, or statistic observed over a shorter period as an equivalent annual figure. It enables comparison across investments, projects, or measurements that span different time horizons. The technique generally assumes that the observed rate persists, at least approximately, over a full year.

In finance, annualizing commonly converts holding period returns into an annualized return. If R_h is the total return over a holding period h (in years), the annualized return is (1 + R_h)^(1/h) − 1. When the period is in days or months, compounding is applied over the corresponding number of periods per year. For example, with a daily return r_d, the annualized return is (1 + r_d)^(252) − 1; with a monthly return r_m, the annualized return (assuming monthly compounding) is (1 + r_m)^(12) − 1. If using a periodic rate r_m for nominal purposes, the annual nominal rate is m * r_m, where m is the number of periods per year, while the effective annual rate is (1 + r_m)^m − 1.

Annualizing also applies to volatility. Annualized volatility equals daily volatility multiplied by the square root of the number of trading days in a year (commonly sqrt(252)).

Other uses include turning an hourly wage into an annual salary by multiplying by hours worked per year, or projecting year-over-year growth rates. Cautions: annualization assumes that the short-term rate is representative of a full year; rates can and do change, and non-stationary data may render an annualization misleading.