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 Accretion of Discount?

Accretion of discount is the increase in the value of a discounted instrument as time passes and the maturity date looms closer. The value of the instrument will accrete (grow) at the interest rate implied by the discounted issuance price, the value at maturity, and the term to maturity.

How Accretion of Discount Works

A bond can be purchased at par, at a premium, or at a discount. Regardless of the purchase price of the bond, however, all bonds mature at par value. The par value is the amount of money that a bond investor will be repaid at maturity. A bond that is purchased at a premium has a value above par. As the bond gets closer to maturity, the value of the bond declines until it is at par on the maturity date. The decrease in value over time is referred to as the amortization of premium.

A bond that is issued at a discount has a value that is less than the par value. As the bond approaches its redemption date, it will increase in value until it converges with the par value at maturity. This increase in value over time is referred to as an accretion of discount. For example, a three-year bond with a face value of $1,000 is issued at $975. Between issuance and maturity, the value of the bond will increase until it reaches its full par value of $1,000, which is the amount that will be paid to the bondholder at maturity.

Special Considerations

Accretion can be accounted for using a straight-line method, whereby the increase is evenly spread throughout the term. Using this method of portfolio accounting, accretion of discount can be said to be a straight-line accumulation of capital gains on a discount bond in anticipation of receipt of par at maturity.

Accretion can also be accounted for using a constant yield, whereby the increase is closest to maturity. The constant yield method is the method required by the Internal Revenue Service (IRS) for calculating the adjusted cost basis from the purchase amount to the expected redemption amount. This method spreads out the gain over the remaining life of the bond, instead of recognizing the gain in the year of the bond’s redemption.

Calculating Accretion

To calculate the amount of accretion, use the formula:

Accretion Amount = Purchase Basis x (YTM / Accrual periods per year) – Coupon Interest

The first step in the constant yield method is determining the yield to maturity (YTM) which is the yield that will be earned on a bond held until it matures. The yield to maturity depends on how frequently the yield is compounded. The IRS allows the taxpayer some flexibility in determining which accrual period to use for computing yield. For example, a bond with a $100 par value and a coupon rate of 2% is issued for $75 with a 10-year maturity date. Let’s assume it is compounded annually for the sake of simplicity. The YTM can, therefore, be calculated as:

• $100 par value = $75 x (1 + r)¹⁰
• $100/$75 = (1 + r)¹⁰
• 1.3333 = (1 + r)¹⁰
• r = 2.92%

Coupon interest on the bond is 2% x $100 par value = $2. Therefore,

• Accretion_period1 = ($75 x 2.92%) – Coupon interest
• Accretion _period1 = $2.19 – $2
• Accretion_period1 = $0.19

The purchase price of $75 represents the bond’s basis at issuance. However, in subsequent periods, the basis becomes the purchase price plus accrued interest. For example, after year 2, the accrual can be calculated as:

• Accretion_period2 = [($75 + $0.19) x 2.92%] – $2
• Accretion_period2 = $0.20

Using this example, one can see that a discount bond has a positive accrual; in other words, the basis accretes, increasing over time from $0.19, $0.20, and so on. Periods 3 to 10 can be calculated in a similar manner, using the former period’s accrual to calculate the current period’s basis.

What Is an Account Statement?

An account statement is a periodic summary of account activity with a beginning date and an ending date. The most commonly known are checking account statements, usually provided monthly, and brokerage account statements, which are provided monthly or quarterly. Monthly credit card bills are also considered account statements.

Understanding Account Statements

Account statements refer to almost any official summary of an account, wherever the account is held. Insurance companies may provide account statements summarizing paid-in cash values, for example. Statements can be generated for almost any type of accounts that represent ongoing transactions where funds are repeatedly exchanged. This can include online payment accounts such as PayPal, credit card accounts, brokerage accounts, and savings accounts.

Utility companies, as well as telephone and subscription television service providers, usually generate account statements for their customers detailing their usage and any overages during the payment cycle. Such statements typically list debits paid, incoming funds or credits received by the account holder, and fees associated with maintaining the account. For example, certain types of savings accounts might incur regular maintenance fees unless a certain minimum balance of funds is maintained in the account. Cable television subscriptions may include state taxes and other surcharges that are included in providing regular service.

How Account Statements Are Used

Account statements should be scrutinized for accuracy, and historical statements are critical for budgeting. A credit or loan account statement, for example, may show not only the outstanding balance due but the interest rate charged on that debt and any fees that have been added during the payment cycle. This can include late charges for payments not received by their due date as well as overdraft fees when bank account holders overspend. Your account statements are a window into your finances.

The statement may also list financial information that relates to the account holder such as their credit score, or the estimated time it will take to completely pay off a debt via installment payments. Alerts and notices to the account holder may also appear on these statements, calling attention to matters with the account that need to be addressed, such unusual charges that should be reviewed and verified.

Red Flags on Account Statements

Anomalous items on an account statement may be a sign the account has been compromised, perhaps through a stolen credit or debit card or through identity thieves who gained access to account information. For example, an account holder or the financial institution might spot a charge for concert tickets or a luxury item that seems out of the ordinary. Account-holders may be able to dispute such out-of-place charges and file a claim that they did not make the purchase themselves. Reviewing your account statements as they come in is a good financial habit that can catch these red flags before they become a financial disaster.

What Is an Auditor?

An auditor is a person authorized to review and verify the accuracy of financial records and ensure that companies comply with tax laws. They protect businesses from fraud, point out discrepancies in accounting methods and, on occasion, work on a consultancy basis, helping organizations to spot ways to boost operational efficiency. Auditors work in various capacities within different industries.

Understanding an Auditor

Auditors assess financial operations and ensure that organizations are run efficiently. They are tasked with tracking cash flow from beginning to end and verifying that an organization’s funds are properly accounted for.

In the case of public companies, the main duty of an auditor is to determine whether financial statements follow generally accepted accounting principles (GAAP). To meet this requirement, auditors inspect accounting data, financial records, and operational aspects of a business and take detailed notes on each step of the process, known as an audit trail.

Once complete, the auditor’s findings are presented in a report that appears as a preface in financial statements. Separate, private reports may also be issued to company management and regulatory authorities as well.

The Securities and Exchange Commission (SEC) demands that the books of all public companies are regularly examined by external, independent auditors, in compliance with official auditing procedures. Official procedures are established by the International Auditing and Assurance Standards Board (IAASB), a committee of the International Federation of Accountants (IFAC).

Unqualified Opinion vs. Qualified Opinion

Auditor reports are usually accompanied by an unqualified opinion. These statements confirm that the company’s financial statements conform to GAAP, without providing judgment or an interpretation.

When an auditor is unable to give an unqualified opinion, they will issue a qualified opinion, a statement suggesting that the information provided is limited in scope and/or the company being audited has not maintained GAAP accounting principles.

Auditors assure potential investors that a company’s finances are in order and accurate, as well as provide a clear picture of a company’s worth to help investors make informed decisions.

Types of Auditors

• Internal auditors are hired by organizations to provide in-house, independent, and objective evaluations of financial and operational business activities, including corporate governance. They report their findings, including tips on how to better run the business, back to senior management.
• External auditors usually work in conjunction with government agencies. They are tasked with providing an objective, public opinion concerning the organization’s financial statements and whether they fairly and accurately represent the organization’s financial position.
• Government auditors maintain and examine records of government agencies and of private businesses or individuals performing activities subject to government regulations or taxation. Auditors employed through the government ensure revenues are received and spent according to laws and regulations. They detect embezzlement and fraud, analyze agency accounting controls, and evaluate risk management.
• Forensic auditors specialize in crime and are used by law enforcement organizations.

Auditor Qualifications

External auditors working for public accounting firms require a Certified Public Accountant (CPA) license, a professional certification awarded by the American Institute of Certified Public Accountants. In addition to this certification, these auditors also need to obtain state CPA certification. Requirements vary, although most states do demand a CPA designation and two years of professional work experience in public accounting.

Qualifications for internal auditors are less rigorous. Internal auditors are encouraged to get CPA accreditation, although it is not always mandatory. Instead, a bachelor’s degree in subjects such as finance and other business disciplines, together with appropriate experience and skills, are often acceptable.

Special Considerations

Auditors are not responsible for transactions that occur after the date of their reports. Moreover, they are not necessarily required to detect all instances of fraud or financial misrepresentation; that responsibility primarily lies with an organization’s management team.

Audits are mainly designed to determine whether a company’s financial statements are “reasonably stated.” In other words, this means that audits do not always cover enough ground to identify cases of fraud. In short, a clean audit offers no guarantee that an organization’s accounting is completely above board.