What Is the Annual Percentage Yield (APY)?

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. Unlike simple interest, compounding interest is calculated periodically and the amount is immediately added to the balance. With each period going forward, the account balance gets a little bigger, so the interest paid on the balance gets bigger as well.

Formula and Calculation of APY

APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year. The formula for calculating APY is:

Where:

• r = period rate 
• n = number of compounding periods

What Annual APY Can Tell You

Any investment is ultimately judged by its rate of return, whether it’s a certificate of deposit (CD), a share of stock, or a government bond. The rate of return is simply the percentage of growth in an investment over a specific period of time, usually one year. But rates of return can be difficult to compare across different investments if they have different compounding periods. One may compound daily, while another compounds quarterly or biannually.

Comparing rates of return by simply stating the percentage value of each over one year gives an inaccurate result, as it ignores the effects of compounding interest. It is critical to know how often that compounding occurs, since the more often a deposit compounds, the faster the investment grows. This is due to the fact that every time it compounds the interest earned over that period is added to the principal balance and future interest payments are calculated on that larger principal amount.

Comparing the APY on 2 Investments

Suppose you are considering whether to invest in a one-year zero-coupon bond that pays 6% upon maturity or a high-yield money market account that pays 0.5% per month with monthly compounding.

At first glance, the yields appear equal because 12 months multiplied by 0.5% equals 6%. However, when the effects of compounding are included by calculating the APY, the money market investment actually yields (1 + .005)^12 – 1 = 0.06168 = 6.17%.

APY vs. APR

APY is similar to the annual percentage rate (APR) used for loans. The APR reflects the effective percentage that the borrower will pay over a year in interest and fees for the loan. APY and APR are both standardized measures of interest rates expressed as an annualized percentage rate.

However, APY takes into account compound interest while APR does not. Furthermore, the equation for APY does not incorporate account fees, only compounding periods. That’s an important consideration for an investor, who must consider any fees that will be subtracted from an investment’s overall return.

Example of APY

If you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.09. If you had been paid simple interest, you would have had $105.

The APY would be (1 + .05/4) * 4 – 1 = .05095 = 5.095%.

It pays 5% a year interest compounded quarterly, and that adds up to 5.095%. That’s not too dramatic. However, if you left that $100 for four years and it was being compounded quarterly then the amount your initial deposit would have grown to $121.99. Without compounding it would have been $120.

X = D(1 + r/n)n*y

= $100(1 + .05/4)4*4

= $100(1.21989)

= $121.99

where:

• X = Final amount
• D = Initial Deposit
• r = period rate 
• n = number of compounding periods per year
• y = number of years

Special Considerations

Compound Interest

The premise of APY is rooted in the concept of compounding or compound interest. Compound interest is the financial mechanism that allows investment returns to earn returns of their own.

Imagine investing $1,000 at 6% compounded monthly. At the start of your investment, you have $1,000.

After one month, your investment will have earned one month worth of interest at 6%. Your investment will now be worth $1,005 ($1,000 * (1 + .06/12)). At this point, we have not yet seen compounding interest.

After the second month, your investment will have earned a second month of interest at 6%. However, this interest is earned on both your initial investment as well as your $5 interest earned last month. Therefore, your return this month will be greater than last month because your investment basis will be higher. Your investment will now be worth $1,010.03 ($1,005 * (1 + .06/12)). Notice that the interest earned this second month is $5.03, different from the $5.00 from last month.

After the third month, your investment will earn interest on the $1,000, the $5.00 earned from the first month, and the $5.03 earned from the second month. This demonstrates the concept of compound interest: the monthly amount earned will continually increase as long as the APY doesn’t decrease and the investment principal is not reduced.

Variable APY vs. Fixed APY

Savings or checking accounts may have either a variable APY or fixed APY. A variable APY is one that fluctuates and changes with macroeconomic conditions, while a fixed APY does not change (or changes much less frequently). One type of APY isn’t necessarily better than the other. While locking into a fixed APY sounds appealing, consider periods when the Federal Reserve is raising rates and APYs increase each month.

Most checking, savings, and money market accounts have variable APYs, though some promotional bank accounts or bank account bonuses may have a higher fixed APY up to a specific level of deposits. For example. a bank may reward 5% APY on the first $500 deposited, then pay 1% APY on all other deposits.

APY and Risk

In general, investors are usually awarded higher yields when they take on greater risk or agree to make sacrifices. The same can be said regarding the APY of checking, saving, and certificate of deposits.

When a consumer holds money in a checking account, the consumer is asking to have their money on demand to pay for expenses. At a given notice, the consumer may need to pull out their debit card, buy groceries, and draw down their checking account. For this reason, checking accounts often have the lowest APY because there is no risk or sacrifice for the consumer.

When a consumer holds money in a savings account, the consumer may not have immediate need. The consumer may need to transfer funds to their checking account before it can be used. Alternatively, you cannot write checks from normal savings accounts. For this reason, savings accounts usually have higher APYs than checking accounts because consumers face greater limits with savings accounts.

Last, when consumers hold a certificate of deposit, the consumer is agreeing to sacrifice liquidity and access to funds in return for a higher APY. The consumer can’t use or spend the money in a CD (or they can after paying a penalty to break the CD). For this reason, the APY on a CD is highest of three as the consumer is being rewarded for sacrificing immediate access to their funds.

The Bottom Line

APY in banking is the actual rate of return you will earn on your checking or savings account. As opposed to simple interest calculations, APY considers the compounding effect of prior interest earned generating future returns. For this reason, APY will often be higher than simple interest, especially if the account compounds often.

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.

What Is Arbitrage?

Arbitrage is the simultaneous purchase and sale of the same or similar asset in different markets in order to profit from tiny differences in the asset’s listed price. It exploits short-lived variations in the price of identical or similar financial instruments in different markets or in different forms.

Arbitrage exists as a result of market inefficiencies, and it both exploits those inefficiencies and resolves them.

Understanding Arbitrage

Arbitrage can be used whenever any stock, commodity, or currency may be purchased in one market at a given price and simultaneously sold in another market at a higher price. The situation creates an opportunity for a risk-free profit for the trader.

Arbitrage provides a mechanism to ensure that prices do not deviate substantially from fair value for long periods of time. With advancements in technology, it has become extremely difficult to profit from pricing errors in the market. Many traders have computerized trading systems set to monitor fluctuations in similar financial instruments. Any inefficient pricing setups are usually acted upon quickly, and the opportunity is eliminated, often in a matter of seconds.

Examples of Arbitrage

As a straightforward example of arbitrage, consider the following: The stock of Company X is trading at $20 on the New York Stock Exchange (NYSE), while, at the same moment, it is trading for $20.05 on the London Stock Exchange (LSE).

A trader can buy the stock on the NYSE and immediately sell the same shares on the LSE, earning a profit of 5 cents per share.

The trader can continue to exploit this arbitrage until the specialists on the NYSE run out of inventory of Company X’s stock, or until the specialists on the NYSE or the LSE adjust their prices to wipe out the opportunity.

A More Complicated Arbitrage Example

A trickier example can be found in currencies markets using triangular arbitrage. In this case, the trader converts one currency to another, converts that second currency to a third bank, and finally converts the third currency back to the original currency.

Suppose you have $1 million and you are provided with the following exchange rates: USD/EUR = 1.1586, EUR/GBP = 1.4600, and USD/GBP = 1.6939.

With these exchange rates, there is an arbitrage opportunity:

1. Sell dollars to buy euros: $1 million ÷ 1.1586 = €863,110
2. Sell euros for pounds: €863,100 ÷ 1.4600 = £591,171
3. Sell pounds for dollars: £591,171 × 1.6939 = $1,001,384
4. Subtract the initial investment from the final amount: $1,001,384 – $1,000,000 = $1,384

From these transactions, you would receive an arbitrage profit of $1,384 (assuming no transaction costs or taxes).

The Bottom Line

Arbitrage is a condition where you can simultaneously buy and sell the same or similar product or asset at different prices, resulting in a risk-free profit.

Economic theory states that arbitrage should not be able to occur because if markets are efficient, there would be no such opportunities to profit. However, in reality, markets can be inefficient and arbitrage can happen. When arbitrageurs identify and then correct such mispricings (by buying them low and selling them high), though, they work to move prices back in line with market efficiency. This means that any arbitrage opportunities that do occur are short-lived.

There are many different arbitrage strategies that exist, some involving complex interrelationships between different assets or securities.

Correction—April 9, 2022: A previous version of this article had miscalculated the complicated arbitrage example.

What Is Asymmetric Information?

Asymmetric information, also known as “information failure,” occurs when one party to an economic transaction possesses greater material knowledge than the other party. This typically manifests when the seller of a good or service possesses greater knowledge than the buyer; however, the reverse dynamic is also possible. Almost all economic transactions involve information asymmetries.

Understanding Asymmetric Information

Asymmetric information exists in certain deals with a seller and a buyer whereby one party is able to take advantage of another. This is usually the case in the sale of an item. For example, if a homeowner wanted to sell their house, they would have more information about the house than the buyer. They might know some floorboards are creaky, the home gets too cold in winter, or that the neighbors are too loud; information that the buyer would not know until after they purchased the house. The buyer, then, might feel they paid too much for the house or would not have purchased it at all if they had this information beforehand.

Asymmetric information can also be viewed as the specialization and division of knowledge, as applied to any economic trade. For example, doctors typically know more about medical practices than their patients. After all, physicians have extensive medical school educational backgrounds that their patients generally don’t have. This principle equally applies to architects, teachers, police officers, attorneys, engineers, fitness instructors, and other trained professionals. Asymmetric information, therefore, is most often beneficial to an economy and a society in increasing efficiency.

Advantages and Disadvantages of Asymmetric Information

Advantages

Asymmetric information isn’t necessarily a bad thing. In fact, growing asymmetrical information is the desired outcome of a healthy market economy. As workers strive to become increasingly specialized in their chosen fields, they become more productive, and can consequently provide greater value to workers in other fields.

For example, a stockbroker’s knowledge is more valuable to a non-investment professional, such as a farmer, who may be interested in confidently trading stocks to prepare for retirement. On the flip side, the stockbroker does not need to know how to grow crops or tend to livestock to feed themself, but rather can purchase the items from a grocery store that are provided by the farmer.

In each of their respective trades, both the farmer and the stockbroker hold superior knowledge over the other, but both benefit from the trade and the division of labor.

One alternative to ever-expanding asymmetric information is for workers to study all fields, rather than specialize in fields where they can provide the most value. However, this is an impractical solution, with high opportunity costs and potentially lower aggregate outputs, which would lower standards of living.

Disadvantages

In some circumstances, asymmetric information may have near fraudulent consequences, such as adverse selection, which describes a phenomenon where an insurance company encounters the probability of extreme loss due to a risk that was not divulged at the time of a policy’s sale.

For example, if the insured hides the fact that they’re a heavy smoker and frequently engage in dangerous recreational activities, this asymmetrical flow of information constitutes adverse selection and could raise insurance premiums for all customers, forcing the healthy to withdraw. The solution is for life insurance providers to perform thorough actuarial work and conduct detailed health screenings, and then charge different premiums to customers based on their honestly disclosed risk profiles.

Special Considerations

To prevent abuse of customers or clients by finance specialists, financial markets often rely on reputation mechanisms. Financial advisors and fund companies that prove to be the most honest and effective stewards of their clients’ assets tend to gain clients, while dishonest or ineffective agents tend to lose clients, face legal damages, or both.