How annualized return is calculated
Annualized return, also called compound annual growth rate (CAGR) for beginning and ending values, is the constant yearly rate that would produce the same total return over the same holding period.
Total return = Ending value ÷ Beginning value − 1
Annualized return = (1 + Total return)1 ÷ Years − 1
The formula uses total return as a decimal, such as 0.21 for 21%. It takes the geometric rate because each year’s gain or loss changes the balance the following year. Dividing 21% by two gives 10.5%, while compounding 10% twice gives the original 21%.
Use a positive beginning value and a nonnegative ending value in the same currency. A total return of −100% corresponds to a zero ending value. Reinvested distributions and any fees you want to count must already be reflected in your inputs. Morningstar’s total return calculation describes how reinvested distributions enter reported returns.
Two worked examples
- 21% over 2 years
- 10.00% annualized
- Growing 10,000 by 10% gives 11,000 after year one and 12,100 after year two.
- 5% over 1 month
- 79.59% annualized
- If the same 5% gain repeated and compounded over 12 months, the full-year gain would be 79.59%. Future months can vary.
How the holding period is measured
Entered years are used as-is. Entered months are divided by 12. Entered days and the actual number of calendar days between two dates are divided by 365.25. An entered month represents one-twelfth of a year, while the span between two calendar dates depends on the dates you choose.
What annualized return leaves out
Two investments can earn the same annualized return while taking very different paths. A steady climb and a sharp drop followed by a recovery can end at the same value. For a market example, this analysis of a quiet SPY rally shows how a meaningful one-session gain coincided with small price swings during the session.
When you contribute, withdraw, or receive a cash distribution during the period, use a method suited to your question. A money-weighted return such as XIRR reflects the amounts and dates of your cash flows. A time-weighted return links returns between external cash flows to measure investment performance separately from those flows. Excel’s XIRR uses a 365-day year. Microsoft’s XIRR documentation describes that convention and the inputs it requires.
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