Annualizing Rolling Returns from Monthly Arithmetic or Log Returns

Summary

The document asks how to annualize returns in rolling five-year estimation windows when the input data are monthly returns. It considers two possible workflows: annualize monthly returns first and then form rolling window returns, or calculate each window’s return before annualizing. The answer emphasizes that the appropriate calculation depends on how the returns were defined.

For arithmetic returns, the response points to the geometric mean as the basis for annualization. For log returns, it says that summing the log returns provides the corresponding aggregation. It recommends calculating monthly returns first and then annualizing them. The exchange does not give a worked numerical example or spell out every convention, such as whether a reported window return is a compounded total or an annualized rate. Readers should therefore apply the distinction between arithmetic and log returns consistently with their chosen return definition.

Key ideas

• The annualization method depends on whether returns are arithmetic or logarithmic.
• For arithmetic returns, the response identifies the geometric mean as the annualization basis.
• Log returns can be aggregated by summation.
• The answer recommends deriving monthly returns before annualizing them.
• The document does not provide a worked example or define every reporting convention.

Tags

# 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 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?

## Answer by Ana B. (score 1)

https://quant.stackexchange.com/a/40302

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

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