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 Accounting Theory?

Accounting theory is a set of assumptions, frameworks, and methodologies used in the study and application of financial reporting principles. The study of accounting theory involves a review of both the historical foundations of accounting practices, as well as the way in which accounting practices are changed and added to the regulatory framework that governs financial statements and financial reporting.

Understanding Accounting Theory

All theories of accounting are bound by the conceptual framework of accounting. This framework is provided by the Financial Accounting Standards Board (FASB), an independent entity that works to outline and establish the key objectives of financial reporting by businesses, both public and private. Further, accounting theory can be thought of as the logical reasoning that helps evaluate and guide accounting practices. Accounting theory, as regulatory standards evolve, also helps develop new accounting practices and procedures.

The most important aspect of accounting theory is usefulness. In the corporate finance world, this means that all financial statements should provide important information that can be used by financial statement readers to make informed business decisions. This also means that accounting theory is intentionally flexible so that it can produce effective financial information, even when the legal environment changes.

In addition to usefulness, accounting theory states that all accounting information should be relevant, reliable, comparable, and consistent. What this essentially means is that all financial statements need to be accurate and adhere to U.S. generally accepted accounting principles (GAAP). Adherence to GAAP allows the preparation of financial statements to be both consistent to a company’s past financials and comparable to the financials of other companies.

Finally, accounting theory requires that all accounting and financial professionals operate under four assumptions. The first assumption states that a business is a separate entity from its owners or creditors. The second affirms the belief that a company will continue to exist and not go bankrupt. The third assumes that all financial statements are prepared with dollar amounts and not with other numbers like units of production. Finally, all financial statements must be prepared on a monthly or annual basis.

Special Considerations

Accounting as a discipline has existed since the 15th century. Since then, both businesses and economies have greatly evolved. Accounting theory is a continuously evolving subject, and it must adapt to new ways of doing business, new technological standards, and gaps that are discovered in reporting mechanisms.

For example, organizations such as the International Accounting Standards Board help create and revise practical applications of accounting theory through modifications to their International Financial Reporting Standards (IFRS). Professionals such as Certified Public Accountants (CPAs) help companies navigate new and established accounting standards.

What Is Accrue?

To accrue means to accumulate over time—most commonly used when referring to the interest, income, or expenses of an individual or business. Interest in a savings account, for example, accrues over time, such that the total amount in that account grows. The term accrue is often related to accrual accounting, which has become the standard accounting practice for most companies.

How Accrue Works

When something financial accrues, it essentially builds up to be paid or received in a future period. Both assets and liabilities can accrue over time. The term “accrue,” when related to finance, is synonymous with an “accrual” under the accounting method outlined by Generally Accepted Accounting Principles (GAAP) and International Financial Reporting Standards (IFRS).

An accrual is an accounting adjustment used to track and record revenues that have been earned but not received, or expenses that have been incurred but not paid. Think of accrued entries as the opposite of unearned entries—with accrued entries, the corresponding financial event has already taken place but payment has not been made or received.

Accepted and mandatory accruals are decided by the Financial Accounting Standards Board (FASB), which controls interpretations of GAAP. Accruals can include accounts payable, accounts receivable, goodwill, future tax liability, and future interest expense. 

Special Considerations

The accrual accounting procedure measures the performance and position of a company by recognizing economic events regardless of when cash transactions occur, giving a better picture of the company’s financial health and causing asset or liability adjustments to “build up” over time.

This is in contrast to the cash method of accounting where revenues and expenses are recorded when the funds are actually paid or received, leaving out revenue based on credit and future liabilities. Cash-based accounting does not require adjustments.

While some very small or new businesses use cash accounting, companies normally prefer the accrual accounting method. Accrual accounting gives a far better picture of a company’s financial situation than cost accounting because it records not only the company’s current finances but also future transactions.

If a company sold $100 worth of product on credit in January, for example, it would want to record that $100 in January under the accrual accounting method rather than wait until the cash is actually received, which may take months or may even become a bad debt.

Types of Accrues

 All accruals fall into one of two categories—either revenue or expense accrual.

Accrued Revenue

Revenue accruals represent income or assets (including non-cash-based ones) yet to be received. These accruals occur when a good or service has been sold by a company, but the payment for it has not been made by the customer. Companies with large amounts of credit card transactions usually have high levels of accounts receivable and high levels of accrued revenue.

Assume that Company ABC hires Consulting Firm XYZ to help on a project that is estimated to take three months to complete. The fee for this job is $150,000, to be paid upon completion. While ABC owes XYZ $50,000 after each monthly milestone, the total fee accrues over the duration of the project instead of being paid in installments.

Accrued Expense

Whenever a business recognizes an expense before it is actually paid, it can make an accrual entry in its general ledger. The expense may also be listed as accrued in the balance sheet and charged against income in the income statement. Common types of accrued expense include:

• Interest expense accruals—these occur when a owes monthly interest on debt prior to receiving the monthly invoice.
• Supplier accruals—these happen if a company receives a good or service from a supplier on credit and plans to pay the supplier at a later date.
• Wage or salary accruals—these expenses happen when a company pays employees prior to the end of the month for a full month of work.

Interest, taxes and other payments sometimes need to be put into accrued entries whenever unpaid obligations should be recognized in the financial statements. Otherwise, the operating expenses for a certain period might be understated, which would result in net income being overstated.

Salaries are accrued whenever a workweek does not neatly correspond with monthly financial reports and payroll. For example, a payroll date may fall on Jan. 28. If employees have to work on January 29, 30, or 31, those workdays still count toward the January operating expenses. Current payroll has not yet accounted for those salary expenses, so an accrued salary account is used.

There are different rationales for accruing specific expenses. The general purpose of an accrual account is to match expenses with the accounting period during which they were incurred. Accrued expenses are also effective in predicting the amount of expenses the company can expect to see in the future.

What is an Actuarial Gain Or Loss?

Actuarial gain or loss refers to an increase or a decrease in the projections used to value a corporation’s defined benefit pension plan obligations. The actuarial assumptions of a pension plan are directly affected by the discount rate used to calculate the present value of benefit payments and the expected rate of return on plan assets. The Financial Accounting Standards Board (FASB) SFAS No. 158 requires the funding status of pension funds to be reported on the plan sponsor’s balance sheet. This means there are periodic updates to the pension obligations, the fund performance and the financial health of the plan. Depending on plan participation rates, market performance and other factors, the pension plan may experience an actuarial gain or loss in their projected benefit obligation.

While those accounting rules require pension assets and liabilities to be marked to market on an entity’s balance sheet, they allow actuarial gains and losses, or changes to actuarial assumptions, to be amortized through comprehensive income in shareholders’ equity rather than flowing directly through the income statement.

Understanding Actuarial Gain Or Loss

Actuarial gains and losses are best understood in the context of overall pension accounting. Except where specifically noted, this definition addresses pension accounting under U.S. generally accepted accounting principles (GAAP). While U.S. GAAP and International Financial Reporting Standards (IFRS) prescribe similar principles measuring pension benefit obligations, there are key differences in how the two standards report pension cost in the income statement, particularly the treatment of actuarial gains and losses.

Funded status represents the net asset or liability related to a company’s defined benefit plans and equals the difference between the value of plan assets and the projected benefit obligation (PBO) for the plan. Valuing plan assets, which are the investments set aside for funding the plan benefits, requires judgment but does not involve the use of actuarial estimates. However, measuring the PBO requires the use of actuarial estimates, and it is these actuarial estimates that give rise to actuarial gains and losses.

There are two primary types of assumptions: economic assumptions that model how market forces affect the plan and demographic assumptions that model how participant behavior is expected to affect the benefits paid. Key economic assumptions include the interest rate used to discount future cash outflows, expected rate of return on plan assets and expected salary increases. Key demographic assumptions include life expectancy, anticipated service periods and expected retirement ages.

Actuarial Gains and Losses Create Volatility in Results

From period to period, a change in an actuarial assumption, particularly the discount rate, can cause a significant increase or decrease in the PBO. If recorded through the income statement, these adjustments potentially distort the comparability of financial results. Therefore, under U.S. GAAP, these adjustments are recorded through other comprehensive income in shareholders’ equity and are amortized into the income statement over time. Under IFRS, these adjustments are recorded through other comprehensive income but are not amortized into the income statement.

Footnote Disclosures Contain Useful Information About Actuarial Assumptions

Accounting rules require detailed disclosures related to pension assets and liabilities, including period-to-period activity in the accounts and the key assumptions used to measure funded status. These disclosures allow financial statement users to understand how a company’s pension plans affect financial position and results of operations relative to prior periods and other companies.