# 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

## 1 Answer

I think it also depends how you defined your returns in the first place: log-returns or arithmetic returns. The formula for geometric mean is for arithmetic returns only, for log returns you can use a simple summation. And usually the procedure is to compute monthly returns first and then annualize them. Refer to https://www.goodreads.com/book/show/1248992.Analysis_of_Financial_Time_Series

• I am doing log-returns. I tried to do it quickly and I got the same results regardless of how I did it (annualize first with compounding and then rolling versus rolling and them annualizing). – Mataunited17 Jun 13 '18 at 13:50