Annualized Return

"Annualized return" just means scaling a return to a yearly rate. The catch: there are two common ways to do it.

1) Geometric (compounded). This is CAGR (Compounded Annual Growth Rate)

$$(1 + R_{total})^{1/years} - 1$$

This is the version we use for multi-year scorecards. It respects compounding.

2) Arithmetic (average). This is common in daily/weekly stats

$$\bar{r}_{daily} \times N$$

This is useful for things like Sharpe/Sortino, where we're annualizing daily returns.

Example (why they differ)

If you go +10% one year and -10% the next, your average annual return is 0%, but your total return is -1%. The compounded annual rate is about -0.5% per year.

So when someone says "annualized return," always ask: geometric or arithmetic?