# What is the correct way to calculate the annualized returns from rolling windows starting from monthly returns?

What is the correct way to calculate the annualized returns in 5-year rolling estimation windows starting from monthly returns?

Is it most correct to first annualize the returns (using the geometric mean for the monthly returns), and then calculate the rolling returns in the estimation window, or opposite?

• I would do it the simple way: compute the rolling returns first and then annualize them by $-1+(1+r)^{\frac{1}{5}}$. – Alex C Jun 11 '18 at 13:10