An annualized total return represents the geometric average amount of money an investment earns each year over a specific period. Calculated using the geometric average, it shows what an investor would earn over some time if the annual return were compounded.
An annualized total return only provides a snapshot of an investment’s performance, and it does not account for its volatility or price fluctuations.
Key Insights
- Geometric Average: An annualized total return is the geometric average amount of money an investment earns each year over a given period.
- Formula: It shows what an investor would earn over a period if the annual return were compounded.
- Calculation: Requires only two main variables: the returns for a given period and the duration the investment was held.
Grasping Annualized Total Return
To understand annualized total return, consider the hypothetical performances of two mutual funds over five years:
- Mutual Fund A: Returns of 3%, 7%, 5%, 12%, and 1%
- Mutual Fund B: Returns of 4%, 6%, 5%, 6%, and 6.7%
Both funds have an annualized rate of return of 5.5%, but Mutual Fund A is more volatile with a standard deviation of 4.2%, whereas Mutual Fund B has a standard deviation of only 1%. This indicates higher risk associated with Mutual Fund A.
Formula and Calculation
The calculation of the annualized rate of return relies on two key variables: the returns for each period and the total duration of the investment. Here’s the formula:
[ \text{Annualized Return} = \left( (1 + r_1) \times (1 + r_2) \times (1 + r_3) \times \ldots \times (1 + r_n) \right)^{ rac{1}{n}} - 1 ]
For example, considering the returns of Mutual Fund A over five years, the calculation is:
[ \text{Annualized Return} = ( (1 + 0.03) \times (1 + 0.07) \times (1 + 0.05) \times (1 + 0.12) \times (1 + 0.01) )^{1/5} - 1 = 1.0553 - 1 = 0.0553, \text{or } 5.53 ext{ ext{ ext{ ext{ ext{ ext{% ext{.}}}}}}} ]
Annualized returns can also be derived from cumulative returns over different periods (e.g., days, months), adjusting the formula accordingly.
Annualized Return vs. Average Return
Simple averages work only with numbers independent of each other. Since annualized returns account for interdependent yearly returns due to compounding, they offer a more accurate performance depiction. For instance, if a loss halves the value, a subsequent 100% return is necessary to break even.
Reporting Annualized Return
Investment Performance Standards dictate that investments without at least a 365-day track record should not annualize their returns to avoid misleading future performance-induced claims.
Calculating Annualized Total Return
The annualized total return captures the average annual performance, sometimes referred to as the Compound Annual Growth Rate (CAGR). Its formula calculates the geometric return, reflecting compounding over time.
Difference Between Annualized Total Return and Average Return
The primary difference is compounding—a key element in calculating the annualized total return, unlike simple averages.
Difference Between Annualized Total Return and CAGR
Though conceptually similar, CAGR is often computed using only the start and end values, whereas annualized total return considers multiple returns periods.
Conclusion
Annualized total return signifies the geometric average amount that an investment earns annually over a certain time frame. By using a geometric average, it accounts for compounding, providing a realistic portrayal of yearly earnings. However, it doesn’t surface the volatility and price fluctuations characteristic of the investment’s history.
Related Terms: geometric average, compounding, standard deviation, cumulative return, compound annual growth rate (CAGR).
