What Is Annualized Total Return?

An annualized total return 🔥is the average annual return earned by an investment over several annual periods. The annualized return formula is calculated as a geometric average to show what an iꦯnvestor would earn over a specified period if the annual return were compounded.

An annualized total return provides only a snapshot of an investment's performance and does not give investors any indication of its 澳洲幸运5官方开奖结果体彩网:volatility or price fluctuations.

Understanding Annualized Total Return

To understand what annualized total return is, it helps to compare the hypothetical performances of two mutual funds. Below is the annualized ra𝄹te of return over fi💎ve years for two funds:

• Mutual Fund A Returns: 3%, 7%, 5%, 12%, and 1%
• Mutual Fund B Returns: 4%, 6%, 5%, 6%, and 6.7%

Both mutual funds have an annualized rate of return of 5.5%. However, in this case, it's important to look beyond the annualized rate of return to how each fund performs. For instance, Mutual Fund A is much more volatile than Mutual Fund B. Its 澳洲幸运5官方开奖结果体彩网:standard deviation is 4.2%, while Mutual Fund B's standard deviat♒ion is only 1%. The amount of volatility can make a significant d𒀰ifference, depending on how long you plan to hold an investment and your strategy and goals.

Annualized Return Formula and Calculation

The formula to calculate the annualized rate of return requires only two variables: the ret🧸urns for a given period and the time the inves🐼tment was held. The formula is:

$\begin{aligned} \text{Annualized Return} = &\big ( (1 + r_1 ) \times (1 + r_2) \times (1 + r_3) \times \\ &\dots \times (1 + r_n) \big ) ^ \frac{1}{n} - 1 \\ \end{aligned}$Annualized Return=​((1+r1​)×(1+r2​)×(1+r3​)×⋯×(1+rn​))n1​−1​

For example, take the annual rates of return of Mutual Fund A above. You'd substitute each r variable with the appropriate return and n with the number of years the investment was hel𒐪d. In this case, five years. The annualized return of Mutual Fund A is calculated as:

$\begin{aligned} \text{Annualized Return} &= \big ( (1 + .03) \times (1 + .07) \times (1 + .05) \times \\ &\quad \quad (1 + .12) \times (1 + .01) \big ) ^ \frac{1}{5} -1 \\ &= 1.309 ^ {0.20} - 1 \\ &= 1.0553 - 1 \\ &= .0553, \text{or } 5.53\% \\ \end{aligned}$Annualized Return​=((1+.03)×(1+.07)×(1+.05)×(1+.12)×(1+.01))51​−1=1.3090.20−1=1.0553−1=.0553,or 5.53%​

An annualized return does not have to be limited to yearly returns. If an investor has a 澳洲幸运5官方开奖结果体彩网:cumulative return for a given period, even if it is a specific number of days, an annualized performanc꧙e figure can be calculated; however, the annual return formula must be slightly adjusted to:

$\begin{aligned} &\text{Annualized Return} = ( 1 + \text{Cumulative Return} ) ^ \frac {365}{ \text{Days Held} } - 1 \\ \end{aligned}$​Annualized Return=(1+Cumulative Return)Days Held365​−1​

For example, assume a mutual fund was held by an investor for 575 days and earned a cumulative return of 23.74%. The annualized rate of r🍃eturn would be:

$\begin{aligned} \text{Annualized Return} &= ( 1 + .2374) ^ \frac{365}{575} - 1 \\ &= 1.145 - 1 \\ &= .145, \text{or } 14.5\% \\ \end{aligned}$Annualized Return​=(1+.2374)575365​−1=1.145−1=.145,or 14.5%​

Difference Between Annualized Return and 🎶Average Return

Average returns differ from annualized returns in that they are calculated by summing the returns for each period and then dividing the result by the numbe𓆉r of periods. For example, you would add the rate of return for each period and divide the result by the number of periods.

The annualized total return uses each period's rate of return (expressed as a percentage), which accounts for compounding. The result is generally less than the average return and more accurately reflects how the investment performed.

Reporting Annualized Return

According to the 澳洲幸运5官方开奖结果体彩网:Global Investment Performanc💯e Standards (GIPS)—a set of standardized, industry-wide principles that guide the ethics of perf💛ormance reporting—any investment that does not have a track record of at least 365 days ca𒈔nnot "ratchet up" its performance to be annualized.

Thus, if a fund has been operating for only six months and has earned꧙ 5%, it is not allowed to say its annualized performance🦋 is approximately 10%, as that would predict future performance instead of stating facts from the past. In other words, calculating an annualized rate of return must be based on historical numbers.

The Bottom Line

Annualized total return represents the geometric average amount that an investment has earned each year over a specific period. By calculating a geometric average, the annualized total return formula accounts for compounding when depicting the yearly earnings the investment would generate over the holding period. While the metric provides a useful snapshot of an investment's performance, it does not reveal volatility and price fluctuations.