What Is Annualized Total Return?

An annualized total return is the geometric average amount of money earned by an investment each year over a given time period. The annualized return formula is calculated as a geometric average to show what an investor would earn over a period of time if the annual return was compounded.

An annualized total return provides only a snapshot of an investment’s performance and does not give investors any indication of its volatility or price fluctuations.

Understanding Annualized Total Return

To understand annualized total return, we’ll compare the hypothetical performances of two mutual funds. Below is the annualized rate of return over a five-year period for the 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%, but Mutual Fund A is much more volatile. Its standard deviation is 4.2%, while Mutual Fund B’s standard deviation is only 1%. Even when analyzing an investment’s annualized return, it is important to review risk statistics.

Annualized Return Formula and Calculation

The formula to calculate annualized rate of return needs only two variables: the returns for a given period of time and the time the investment 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 returns of Mutual Fund A above. An analyst substitutes each of the “r” variables with the appropriate return, and “n” with the number of years the investment was held. 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 cumulative return for a given period, even if it is a specific number of days, an annualized performance 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 return 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

Calculations of simple averages only work when numbers are independent of each other. The annualized return is used because the amount of investment lost or gained in a given year is interdependent with the amount from the other years under consideration because of compounding.

For example, if a mutual fund manager loses half of her client’s money, she has to make a 100% return to break even. Using the more accurate annualized return also gives a clearer picture when comparing various mutual funds or the return of stocks that have traded over different time periods. 

Reporting Annualized Return

According to the Global Investment Performance Standards (GIPS)—a set of standardized, industry-wide principles that guide the ethics of performance reporting—any investment that does not have a track record of at least 365 days cannot “ratchet up” its performance to be annualized.

Thus, if a fund has been operating for only six months and earned 5%, it is not allowed to say its annualized performance is approximately 10% since that is predicting 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 that 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.

What Is the Asian Development Bank?

The Asian Development Bank’s primary mission is to “foster economic growth and cooperation” among countries in the Asia-Pacific Region. Founded in 1966 and based in Manila, Philippines, the ADB assists members and partners by providing loans, technical assistance, grants, and equity investments to promote social and economic development.

The ADB has been responsible for major projects in the region and raises capital regularly through the international bond markets. The ADB also relies on member contributions, retained earnings from lending, and the repayment of loans for the funding of the organization.

How the Asian Development Bank Works

The Asian Development Bank provides assistance to its developing member countries, the private sector, and public-private partnerships through grants, loans, technical assistance, and equity investments to promote development. The ADB regularly facilitates policy dialogues and provides advisory services. They also use co-financing operations that tap official, commercial, and export credit sources while providing assistance.

Membership in the ADB is open to members and associate members of the United Nations Economic Commission for Asia and the Far East. It’s also open to other regional countries and non-regional developed countries that are members of the U.N. or of any of its specialized agencies. 

Financing Provided by the Asian Development bank

The ADB provides both private financing and sovereign (public) financing. Private sector efforts focus on projects that help promote private investments in the region that will have significant development impact and will lead to accelerated, sustainable, and inclusive growth. Public-sector financing provides funding for member countries with flexibility in determining how they can achieve development goals.

In 2021, the ADB committed nearly US$13.5 billion to help its developing member countries address the impacts of the COVID-19 crisis and address vaccination needs, and has mobilized a further $12.9 billion in co-financing from partners. Through a $9 billion Asia Pacific Vaccine Access Facility, or APVAX, announced in December 2020, the ADB provided funding for vaccine procurement, logistics, and distribution.

The total private financing portfolio consisted of $14.2 billion at the end of 2021. In terms of sovereign financing, ADB’s portfolio stood at $104 billion by the end of 2021, consisting of 713 loans, 392 grants, 915 TA projects, one guarantee, and 1 equity investment.

Structure of the Asian Development Bank

According to ADB’s website, “the Agreement Establishing the Asian Development Bank, known as the ADB Charter, vests all the powers of the institution in the Board of Governors, which in turn delegates some of these powers to the Board of Directors. The Board of Governors meets formally once a year during ADB’s Annual Meeting.” The ADB’s highest policy-making body is its Board of Governors, which comprises one representative from each member.

The two largest shareholders of the Asian Development Bank are the United States and Japan. Although the majority of the Bank’s members are from the Asia-Pacific region, the industrialized nations are also well-represented. Regional development banks usually work in harmony with both the International Monetary Fund (IMF) and the World Bank in their activities.

Asian Development Bank Country Relationships

When ADB was founded in 1966, it consisted of 31 members. Since then, membership has grown to 68 members, which is made up of 48 regional and 19 non-regional members. Membership as of 2022 includes:

What Is an Annual Return?

The annual return is the return that an investment provides over a period of time, expressed as a time-weighted annual percentage. Sources of returns can include dividends, returns of capital and capital appreciation. The rate of annual return is measured against the initial amount of the investment and represents a geometric mean rather than a simple arithmetic mean.

Understanding Annual Return

The de facto method for comparing the performance of investments with liquidity, an annual return can be calculated for various assets, which include stocks, bonds, funds, commodities and some types of derivatives. This process is a preferred method, considered to be more accurate than a simple return, as it includes adjustments for compounding interest. Different asset classes are considered to have different strata of annual returns.

Annual Returns on Stocks

Also known as an annualized return, the annual return expresses the stock’s increase in value over a designated period of time. In order to calculate an annual return, information regarding the current price of the stock and the price at which it was purchased are required. If any splits have occurred, the purchase price needs to be adjusted accordingly. Once the prices are determined, the simple return percentage is calculated first, with that figure ultimately being annualized. The simple return is just the current price minus the purchase price, divided by the purchase price.

Example Annual Return Calculation


$\begin{aligned} &\text{CAGR} = \left ( \left ( \frac{ \text{Ending Value} }{ \text{Beginning Value } } \right ) ^ \frac{ 1 }{ \text{Years} } \right ) – 1 \\ &\textbf{where:} \\ &\text{CAGR} = \text{compound annual growth rate} \\ &\text{Years} = \text{holding period, in years} \\ \end{aligned}$​CAGR=((Beginning Value Ending Value​)Years1​)−1where:CAGR=compound annual growth rateYears=holding period, in years​

Consider an investor that purchases a stock on Jan. 1, 2000, for $20. The investor then sells it on Jan. 1, 2005, for $35 – a $15 profit. The investor also receives a total of $2 in dividends over the five-year holding period. In this example, the investor’s total return over five years is $17, or (17/20) 85% of the initial investment. The annual return required to achieve 85% over five years follows the formula for the compound annual growth rate (CAGR):


$\begin{aligned} &\left ( \left ( \frac { 37 }{ 20 } \right ) ^ \frac{ 1 }{ 5 } \right ) – 1 = 13.1\% \text{ annual return} \\ \end{aligned}$​((2037​)51​)−1=13.1% annual return​

The annualized return varies from the typical average and shows the real gain or loss on an investment, as well as the difficulty in recouping losses. For instance, losing 50% on an initial investment requires a 100% gain the next year in order to make up the difference. Because of the sizable difference in gains and losses that can occur, annualized returns help even out investment results for better comparison. 

Annual Returns on a 401K

The calculation differs when determining the annual return of a 401K during a specified year. First, the total return must be calculated. The starting value for the time period being examined is needed, along with the final value. Before performing the calculations, any contributions to the account during the time period in question must be subtracted from the final value.

Once the adjusted final value is determined, it is divided by the starting balance. Finally, subtract 1 from the result and multiply that amount by 100 to determine the percentage total return.

What Is an Annualized Rate of Return?

An annualized rate of return is calculated as the equivalent annual return an investor receives over a given period. The Global Investment Performance Standards dictate that returns of portfolios or composites for periods of less than one year may not be annualized. This prevents “projected” performance in the remainder of the year from occurring.

Understanding Annualized Rate

Annualized returns are returns over a period scaled down to a 12-month period. This scaling process allows investors to objectively compare the returns of any assets over any period.

Calculation Using Annual Data

Calculating the annualized performance of an investment or index using yearly data uses the following data points:

P = principal, or initial investment

G = gains or losses

n = number of years

AP = annualized performance rate

The generalized formula, which is exponential to take into account compound interest over time, is:

AP = ((P + G) / P) ^ (1 / n) – 1

Annualized Rate of Return Examples

For example, assume an investor invested $50,000 into a mutual fund and, four years later, the investment is worth $75,000. This is a $25,000 gain in four years. Thus, the annualized performance is:

AP = (($50,000 + $25,000) / $50,000) ^ (1/4) – 1

In this example, the annualized performance is 10.67 percent.

A $25,000 gain on a $50,000 investment over four years is a 50 percent return. It is inaccurate to say the annualized return is 12.5 percent, or 50 percent divided by four because this does not take into effect compound interest. If reversing the 10.67 percent result to compound over four years, the result is exactly what is expected:

$75,000 = $50,000 x (1 + 10.67%) ^ 4

It is important not to confuse annualized performance with annual performance. The annualized performance is the rate at which an investment grows each year over the period to arrive at the final valuation. In this example, a 10.67 percent return each year for four years grows $50,000 to $75,000. But this says nothing about the actual annual returns over the four-year period. Returns of 4.5 percent, 13.1 percent, 18.95 percent and 6.7 percent grow $50,000 into approximately $75,000. Also, returns of 15 percent, -7.5 percent, 28 percent, and 10.2 percent provide the same result.

Using Days in the Calculation

Industry standards for most investments dictate the most precise form of annualized return calculation, which uses days instead of years. The formula is the same, except for the exponent:

AP = ((P + G) / P) ^ (365 / n) – 1

Assume from the previous example that the fund returned $25,000 over a 1,275-day period. The annualized return is then:

AP = (($50,000 + $25,000) / $50,000) ^ (365/1275) – 1

The annualized performance in this example is 12.31 percent.