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 a 12B-1 Plan?

A 12B-1 plan is a plan structured by mutual fund companies for the distribution of funds through intermediaries. 12B-1 plans provide mapping for the partnerships between distributors and intermediaries who help to ensure the sale of a fund. Sales commission schedules and 12B-1 distribution expenses are the primary components driving a 12B-1 plan.

Understanding the 12B-1 Plan

12B-1 plans facilitate the partnerships between distributors and intermediaries offering mutual fund shares. 12B-1 plans are primarily focused on open-end mutual funds, which have multiple class structures for sales charges and distribution expenses. Mutual fund companies consider two types of 12B-1 charges in their 12B-1 plans, sales commissions, and 12B-1 expenses.

Sales Commissions

Sales commission schedules are structured to provide compensation to intermediaries for transacting mutual funds. These partnerships can help to increase demand for funds by being marketed from a full-service broker-dealer who facilitates the transaction for a sales load fee. These fees are paid to the broker and are not associated with annual fund operating expenses.

Sales loads are structured to vary across share classes. Share classes can include front-end, back-end, and level-load sales charges. These sales charges are associated with individual retail share classes which typically include Class A, B, and C shares.

12B-1 Expenses

12B-1 expenses paid from the mutual fund to distributors and intermediaries are also a key part of a 12B-1 plan. To market and distribute open-end mutual fund shares, mutual fund companies work with distributors to get their funds listed with discount brokerages and financial advisor platforms. Distributors help fund companies partner with the full-service brokers that transact their funds at the agreed-upon sales load schedule.

Mutual fund companies will pay 12B-1 fees from a mutual fund to compensate distributors. In some cases, funds may also be structured with a low-level load that is paid to financial advisors annually during the course of an investor’s holding period.

Financial industry legislation typically restricts 12B-1 fees to 1% of the current value of the investment on an annual basis, but fees generally fall somewhere between 0.25% and 1%. In most cases, fund companies will have higher 12B-1 fees on share classes paying a lower sales charge, and lower 12B-1 fees on share classes with higher sales charges. This helps to balance out the compensation paid to intermediary brokers while also providing for payment to distribution partners.

Disclosure

Mutual fund companies are required to provide full disclosure on their sales load schedules and 12B-1 annual fund expenses in the fund’s prospectus. The prospectus is one aspect of documentation required for the mutual fund’s registration and is also the key offering document providing information on the fund for investors. 12B-1 plans and any changes to their expense structuring must be approved by the fund’s board of directors and amended in its prospectus filed with the Securities and Exchange Commission.

What Is the Addition Rule for Probabilities?

The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two non-mutually exclusive events happening.

The first formula is just the sum of the probabilities of the two events. The second formula is the sum of the probabilities of the two events minus the probability that both will occur.

The Formulas for the Addition Rules for Probabilities Is

Mathematically, the probability of two mutually exclusive events is denoted by:


$P(Y \text{ or } Z) = P(Y)+P(Z)$P(Y or Z)=P(Y)+P(Z)

Mathematically, the probability of two non-mutually exclusive events is denoted by:


$P(Y \text{ or } Z) = P(Y) + P(Z) – P(Y \text{ and } Z)$P(Y or Z)=P(Y)+P(Z)−P(Y and Z)

What Does the Addition Rule for Probabilities Tell You?

To illustrate the first rule in the addition rule for probabilities, consider a die with six sides and the chances of rolling either a 3 or a 6. Since the chances of rolling a 3 are 1 in 6 and the chances of rolling a 6 are also 1 in 6, the chance of rolling either a 3 or a 6 is:

1/6 + 1/6 = 2/6 = 1/3

To illustrate the second rule, consider a class in which there are 9 boys and 11 girls. At the end of the term, 5 girls and 4 boys receive a grade of B. If a student is selected by chance, what are the odds that the student will be either a girl or a B student? Since the chances of selecting a girl are 11 in 20, the chances of selecting a B student are 9 in 20 and the chances of selecting a girl who is a B student are 5/20, the chances of picking a girl or a B student are:

11/20 + 9/20 – 5/20 =15/20 = 3/4

In reality, the two rules simplify to just one rule, the second one. That’s because in the first case, the probability of two mutually exclusive events both happening is 0. In the example with the die, it’s impossible to roll both a 3 and a 6 on one roll of a single die. So the two events are mutually exclusive.

Mutual Exclusivity

Mutually exclusive is a statistical term describing two or more events that cannot coincide. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.  For a basic example, consider the rolling of dice. You cannot roll both a five and a three simultaneously on a single die. Furthermore, getting a three on an initial roll has no impact on whether or not a subsequent roll yields a five. All rolls of a die are independent events.

What Is an Annual Report?

An annual report is a document that public corporations must provide annually to shareholders that describes their operations and financial conditions. The front part of the report often contains an impressive combination of graphics, photos, and an accompanying narrative, all of which chronicle the company’s activities over the past year and may also make forecasts about the future of the company. The back part of the report contains detailed financial and operational information.

Understanding Annual Reports

Annual reports became a regulatory requirement for public companies following the stock market crash of 1929 when lawmakers mandated standardized corporate financial reporting. The intent of the required annual report is to provide public disclosure of a company’s operating and financial activities over the past year. The report is typically issued to shareholders and other stakeholders who use it to evaluate the firm’s financial performance and to make investment decisions.

Typically, an annual report will contain the following sections:

In the U.S., a more detailed version of the annual report is referred to as Form 10-K and is submitted to the U.S. Securities and Exchange Commission (SEC). Companies may submit their annual reports electronically through the SEC’s EDGAR database. Reporting companies must send annual reports to their shareholders when they hold annual meetings to elect directors. Under the proxy rules, reporting companies are required to post their proxy materials, including their annual reports, on their company websites.

Special Considerations

The annual report contains key information on a company’s financial position that can be used to measure:

• A company’s ability to pay its debts as they come due
• Whether a company made a profit or loss in its previous fiscal year
• A company’s growth over a number of years
• How much of earnings are retained by a company to grow its operations
• The proportion of operational expenses to revenue generated

The annual report also determines whether the information conforms to the generally accepted accounting principles (GAAP). This confirmation will be highlighted as an “unqualified opinion” in the auditor’s report section.

Fundamental analysts also attempt to understand a company’s future direction by analyzing the details provided in its annual report.

Mutual Fund Annual Reports

In the case of mutual funds, the annual report is a required document that is made available to a fund’s shareholders on a fiscal year basis. It discloses certain aspects of a mutual fund’s operations and financial condition. In contrast to corporate annual reports, mutual fund annual reports are best described as “plain vanilla” in terms of their presentation.

A mutual fund annual report, along with a fund’s prospectus and statement of additional information, is a source of multi-year fund data and performance, which is made available to fund shareholders as well as to prospective fund investors. Unfortunately, most of the information is quantitative rather than qualitative, which addresses the mandatory accounting disclosures required of mutual funds.

All mutual funds that are registered with the SEC are required to send a full report to all shareholders every year. The report shows how well the fund fared over the fiscal year. Information that can be found in the annual report includes:

• Table, chart, or graph of holdings by category (e.g., type of security, industry sector, geographic region, credit quality, or maturity)
• Audited financial statements, including a complete or summary (top 50) list of holdings
• Condensed financial statements
• Table showing the fund’s returns for 1-, 5- and 10-year periods
• Management’s discussion of fund performance
• Management information about directors and officers, such as name, age, and tenure
• Remuneration or compensation paid to directors, officers, and others

The Bottom Line

Public companies must produce annual reports to show their current financial conditions and operations. Annual reports can be used to examine a company’s financial position and, possibly, understand what direction it will move in the future. These reports function differently for mutual funds; in this case, they are made available each fiscal year and are typically simpler.