Annualisation
Converting a return or volatility measured over a shorter period, such as a day, into an equivalent yearly figure so that different instruments and timeframes can be compared.
Annual volatility = daily σ × √252 Annual return = (1 + daily r)²⁵² − 1
Annualisation puts statistics on a common yearly scale. Returns are annualised by compounding: an average daily return r becomes (1 + r)²⁵² − 1 over a year of about 252 trading days. Volatility is annualised with the square root of time: daily standard deviation × √252, weekly × √52, monthly × √12.
The square-root rule assumes returns are independent from one period to the next. Real returns only roughly behave that way. Trends, mean reversion, volatility that clusters and occasional large jumps all make the yearly figure an approximation, so it is a convention for comparison rather than a forecast.
Annualised figures can also flatter short samples. Three good weeks, annualised, can produce a yearly number that no actual year will deliver. Always state the period a statistic was measured over alongside its annualised value.
On the desk
Daily returns with a standard deviation of 1.13% annualise to 1.13% × √252 ≈ 17.9% volatility. An average daily return of 0.05% compounds to (1.0005)²⁵² − 1 ≈ 13.4% a year, a figure that assumes every day is an average day.