What Is an Anomaly?

In economics and finance, an anomaly is when the actual result under a given set of assumptions is different from the expected result predicted by a model. An anomaly provides evidence that a given assumption or model does not hold up in practice. The model can either be a relatively new or older model.

Understanding Anomalies

In finance, two common types of anomalies are market anomalies and pricing anomalies. Market anomalies are distortions in returns that contradict the efficient market hypothesis (EMH). Pricing anomalies are when something—for example, a stock—is priced differently than how a model predicts it will be priced.

Common market anomalies include the small-cap effect and the January effect. The small-cap effect refers to the small company effect, where smaller companies tend to outperform larger ones over time. The January effect refers to the tendency of stocks to return much more in the month of January than in others.

Anomalies also often occur with respect to asset pricing models, in particular, the capital asset pricing model (CAPM). Although the CAPM was derived by using innovative assumptions and theories, it often does a poor job of predicting stock returns. The numerous market anomalies that were observed after the formation of the CAPM helped form the basis for those wishing to disprove the model. Although the model may not hold up in empirical and practical tests, it still does hold some utility.

Anomalies tend to be few and far between. In fact, once anomalies become publicly known, they tend to quickly disappear as arbitragers seek out and eliminate any such opportunity from occurring again.

Types of Market Anomalies

In financial markets, any opportunity to earn excess profits undermines the assumptions of market efficiency, which states that prices already reflect all relevant information and so cannot be arbitraged.

January Effect

The January effect is a rather well-known anomaly. According to the January effect, stocks that underperformed in the fourth quarter of the prior year tend to outperform the markets in January. The reason for the January effect is so logical that it is almost hard to call it an anomaly. Investors will often look to jettison underperforming stocks late in the year so that they can use their losses to offset capital gains taxes (or to take the small deduction that the IRS allows if there is a net capital loss for the year). Many people call this event tax-loss harvesting.

As selling pressure is sometimes independent of the company’s actual fundamentals or valuation, this “tax selling” can push these stocks to levels where they become attractive to buyers in January.

Likewise, investors will often avoid buying underperforming stocks in the fourth quarter and wait until January to avoid getting caught up in the tax-loss selling. As a result, there is excess selling pressure before January and excess buying pressure after Jan. 1, leading to this effect.

September Effect

The September effect refers to historically weak stock market returns for the month of September. There is a statistical case for the September effect depending on the period analyzed, but much of the theory is anecdotal. It is generally believed that investors return from summer vacation in September ready to lock in gains as well as tax losses before the end of the year.

There is also a belief that individual investors liquidate stocks going into September to offset schooling costs for children. As with many other calendar effects, the September effect is considered a historical quirk in the data rather than an effect with any causal relationship. 

Days of the Week Anomalies

Efficient market supporters hate the “Days of the Week” anomaly because it not only appears to be true, but it also makes no sense. Research has shown that stocks tend to move more on Fridays than Mondays and that there is a bias toward positive market performance on Fridays. It is not a huge discrepancy, but it is a persistent one.

The Monday effect is a theory which states that returns on the stock market on Mondays will follow the prevailing trend from the previous Friday. Therefore, if the market was up on Friday, it should continue through the weekend and, come Monday, resume its rise. The Monday effect is also known as the “weekend effect.”

On a fundamental level, there is no particular reason that this should be true. Some psychological factors could be at work. Perhaps an end-of-week optimism permeates the market as traders and investors look forward to the weekend. Alternatively, perhaps the weekend gives investors a chance to catch up on their reading, stew and fret about the market, and develop pessimism going into Monday.

Superstitious Indicators

Aside from calendar anomalies, there are some non-market signals that some people believe will accurately indicate the direction of the market. Here is a short list of superstitious market indicators:

• The Super Bowl Indicator: When a team from the old American Football League wins the game, the market will close lower for the year. When an old National Football League team wins, the market will end the year higher. Silly as it may seem, the Super Bowl indicator was correct almost three-quarters of the time over a 53-year period ending in 2021. However, the indicator has one limitation: It contains no allowance for an expansion-team victory!
• The Hemline Indicator: The market rises and falls with the length of skirts. Sometimes this indicator is referred to as the “bare knees, bull market” theory. To its merit, the hemline indicator was accurate in 1987, when designers switched from miniskirts to floor-length skirts just before the market crashed. A similar change also took place in 1929, but many argue as to which came first, the crash or the hemline shifts.
• The Aspirin Indicator: Stock prices and aspirin production are inversely related. This indicator suggests that when the market is rising, fewer people need aspirin to heal market-induced headaches. Lower aspirin sales should indicate a rising market.

What Is the Arbitrage Pricing Theory (APT)?

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset’s returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced.

The Formula for the Arbitrage Pricing Theory Model Is


$\begin{aligned} &\text{E(R)}_\text{i} = E(R)_z + (E(I) – E(R)_z) \times \beta_n\\ &\textbf{where:}\\ &\text{E(R)}_\text{i} = \text{Expected return on the asset}\\ &R_z = \text{Risk-free rate of return}\\ &\beta_n = \text{Sensitivity of the asset price to macroeconomic} \\ &\text{factor}\textit{ n}\\ &Ei = \text{Risk premium associated with factor}\textit{ i}\\ \end{aligned}$​E(R)i​=E(R)z​+(E(I)−E(R)z​)×βn​where:E(R)i​=Expected return on the assetRz​=Risk-free rate of returnβn​=Sensitivity of the asset price to macroeconomicfactor nEi=Risk premium associated with factor i​

The beta coefficients in the APT model are estimated by using linear regression. In general, historical securities returns are regressed on the factor to estimate its beta.

How the Arbitrage Pricing Theory Works

The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (CAPM). Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.

However, this is not a risk-free operation in the classic sense of arbitrage, because investors are assuming that the model is correct and making directional trades—rather than locking in risk-free profits.

Mathematical Model for the APT

While APT is more flexible than the CAPM, it is more complex. The CAPM only takes into account one factor—market risk—while the APT formula has multiple factors. And it takes a considerable amount of research to determine how sensitive a security is to various macroeconomic risks.

The factors as well as how many of them are used are subjective choices, which means investors will have varying results depending on their choice. However, four or five factors will usually explain most of a security’s return. (For more on the differences between the CAPM and APT, read more about how CAPM and arbitrage pricing theory differ.)

APT factors are the systematic risk that cannot be reduced by the diversification of an investment portfolio. The macroeconomic factors that have proven most reliable as price predictors include unexpected changes in inflation, gross national product (GNP), corporate bond spreads and shifts in the yield curve. Other commonly used factors are gross domestic product (GDP), commodities prices, market indices, and exchange rates.

Example of How Arbitrage Pricing Theory Is Used

For example, the following four factors have been identified as explaining a stock’s return and its sensitivity to each factor and the risk premium associated with each factor have been calculated:

• Gross domestic product (GDP) growth: ß = 0.6, RP = 4%
• Inflation rate: ß = 0.8, RP = 2%
• Gold prices: ß = -0.7, RP = 5%
• Standard and Poor’s 500 index return: ß = 1.3, RP = 9%
• The risk-free rate is 3%

Using the APT formula, the expected return is calculated as:

• Expected return = 3% + (0.6 x 4%) + (0.8 x 2%) + (-0.7 x 5%) + (1.3 x 9%) = 15.2%

What Is At The Money (ATM)?

At the money (ATM) is a situation where an option’s strike price is identical to the current market price of the underlying security. An ATM option has a delta of ±0.50, positive if it is a call, negative for a put.

Both call and put options can be simultaneously ATM. For example, if XYZ stock is trading at $75, then the XYZ 75 call option is ATM and so is the XYZ 75 put option. ATM options have no intrinsic value, but will still have extrinsic or time value prior to expiration, and may be contrasted with either in the money (ITM) or out of the money (OTM) options.

Understanding At The Money (ATM)

At the money (ATM), sometimes referred to as “on the money”, is one of three terms used to describe the relationship between an option’s strike price and the underlying security’s price, also called the option’s moneyness.

Options can be in the money (ITM), out of the money (OTM), or ATM. ITM means the option has intrinsic value and OTM means it doesn’t. Simply put, ATM options are not in a position to profit if exercised, but still have value—there is still time before they expire so they may yet end up ITM.

The intrinsic value for a call option is calculated by subtracting the strike price from the underlying security’s current price. The intrinsic value for a put option, on the other hand, is calculated by subtracting the underlying asset’s current price from its strike price.

A call option is ITM when the option’s strike price is less than the underlying security’s current price. Conversely, a put option is ITM when the option’s strike price is greater than the underlying security’s stock price. Meanwhile, a call option is OTM when its strike price is greater than the current underlying security’s price and a put option is OTM when its strike price is less than the underlying asset’s current price.

Special Considerations

Options that are ATM are often used by traders to construct spreads and combinations. Straddles, for instance, will typically involve buying (or selling) both an ATM call and put.

ATM options are the most sensitive to various risk factors, known as an option’s “Greeks”. ATM options have a ±0.50 delta, but have the greatest amount of gamma, meaning that as the underlying moves its delta will move away from ±0.50 rapidly, and most rapidly as time to expiration nears.

ATM options are the most sensitive to time decay, as represented by an option’s theta. Moreover, their prices are most responsive to changes in volatility, especially for farther maturities, and is expressed by an option’s vega. Finally, ATM options are also most sensitive to changes in interest rates, as measured by the rho.

At The Money (ATM) and Near The Money

The term “near the money” is sometimes used to describe an option that is within 50 cents of being ATM. For example, assume an investor purchases a call option with a strike price of $50.50 and the underlying stock price is trading at $50. In this case, the call option is said to be near the money.

In the above example, the option would be near the money if the underlying stock price was trading between about $49.50 and $50.50. Near the money and ATM options are attractive when traders expect a big movement. Options that are even further OTM may also see a jump when a swing is anticipated.

Options Pricing for At The Money (ATM) Options

An option’s price is made up of intrinsic and extrinsic value. Extrinsic value is sometimes called time value, but time is not the only factor to consider when trading options. Implied volatility also plays a significant role in options pricing. 

Similar to OTM options, ATM options only have extrinsic value because they possess no intrinsic value. For example, assume an investor purchases an ATM call option with a strike price of $25 for a price of 50 cents. The extrinsic value is equivalent to 50 cents and is largely affected by the passage of time and changes in implied volatility.

Assuming volatility and the price stay steady, the closer the option gets to expiry the less extrinsic value it has. If the price of the underlying moves above the strike price to $27, the option now has $2 of intrinsic value, plus whatever extrinsic value remains.

What Is an American Depositary Receipt (ADR)?

The term American depositary receipt (ADR) refers to a negotiable certificate issued by a U.S. depositary bank representing a specified number of shares—usually one share—of a foreign company’s stock. The ADR trades on U.S. stock markets as any domestic shares would.

ADRs offer U.S. investors a way to purchase stock in overseas companies that would not otherwise be available. Foreign firms also benefit, as ADRs enable them to attract American investors and capital without the hassle and expense of listing on U.S. stock exchanges.

How American Depositary Receipts (ADRs) Work

American depositary receipts are denominated in U.S. dollars. The underlying security is held by a U.S. financial institution, often by an overseas branch. These securities are priced and traded in dollars and cleared through U.S. settlement systems.

In order to begin offering ADRs, a U.S. bank must purchase shares on a foreign exchange. The bank holds the stock as inventory and issues an ADR for domestic trading. ADRs list on either the New York Stock Exchange (NYSE) or the Nasdaq, but they are also sold over-the-counter (OTC).

U.S. banks require that foreign companies provide them with detailed financial information. This requirement makes it easier for American investors to assess a company’s financial health.

Types of American Depositary Receipts

American depositary receipts come in two basic categories:

Sponsored ADRs

A bank issues a sponsored ADR on behalf of the foreign company. The bank and the business enter into a legal arrangement. The foreign company usually pays the costs of issuing an ADR and retains control over it, while the bank handles the transactions with investors. Sponsored ADRs are categorized by what degree the foreign company complies with Securities and Exchange Commission (SEC) regulations and American accounting procedures.

Unsponsored ADRs

A bank also issues an unsponsored ADR. However, this certificate has no direct involvement, participation, or even permission from the foreign company. Theoretically, there could be several unsponsored ADRs for the same foreign company, issued by different U.S. banks. These different offerings may also offer varying dividends. With sponsored programs, there is only one ADR, issued by the bank working with the foreign company.

One primary difference between the two types of ADRs is where they trade. All except the lowest level of sponsored ADRs register with the SEC and trade on major U.S. stock exchanges. Unsponsored ADRs will trade only over the counter. Unsponsored ADRs never include voting rights.

ADR Levels

ADRs are additionally categorized into three levels, depending on the extent to which the foreign company has accessed the U.S. markets.

Level I

This is the most basic type of ADR where foreign companies either don’t qualify or don’t want to have their ADR listed on an exchange. This type of ADR can be used to establish a trading presence but not to raise capital.

Level I ADRs found only on the over-the-counter market have the loosest requirements from the Securities and Exchange Commission (SEC) and they are typically highly speculative. While they are riskier for investors than other types of ADRs, they are an easy and inexpensive way for a foreign company to gauge the level of U.S. investor interest in its securities.

Level II

As with Level I ADRs, Level II ADRs can be used to establish a trading presence on a stock exchange, and they can’t be used to raise capital. Level II ADRs have slightly more requirements from the SEC than do Level I ADRs, but they get higher visibility and trading volume. 

Level III

Level III ADRs are the most prestigious. With these, an issuer floats a public offering of ADRs on a U.S. exchange. They can be used to establish a substantial trading presence in the U.S. financial markets and raise capital for the foreign issuer. Issuers are subject to full reporting with the SEC.

American Depositary Receipt Pricing and Costs

An ADR may represent the underlying shares on a one-for-one basis, a fraction of a share, or multiple shares of the underlying company. The depositary bank will set the ratio of U.S. ADRs per home-country share at a value that they feel will appeal to investors. If an ADR’s value is too high, it may deter some investors. Conversely, if it is too low, investors may think the underlying securities resemble riskier penny stocks.

Because of arbitrage, an ADR’s price closely tracks that of the company’s stock on its home exchange. Remember that arbitrage is buying and selling the same asset at the same time in different markets. This allows traders to profit from any differences in the asset’s listed price. 

ADR Fees

Investing in an ADR may incur additional fees that are not charged for domestic stocks. The depositary bank that holds the underlying stock may charge a fee, known as a custody fee, to cover the cost of creating and issuing an ADR.

This fee will be outlined in the ADR prospectus, and typically ranges from one to three cents per share. The fee will be either deducted from dividends, or passed on to the investor’s brokerage firm.

ADRs and Taxes

Holders of ADRs realize any dividends and capital gains in U.S. dollars. However, dividend payments are net of currency conversion expenses and foreign taxes. Usually, the bank automatically withholds the necessary amount to cover expenses and foreign taxes.

Since this is the practice, American investors would need to seek a credit from the IRS or a refund from the foreign government’s taxing authority to avoid double taxation on any capital gains realized.

Those interested in learning more about ADRs and other financial topics may want to consider enrolling in one of the best investing courses currently available.

Advantages and Disadvantages of American Depositary Receipts

As with any investment, there are distinct advantages and disadvantages of investing in ADRs. We’ve listed some of the main ones below.

Advantages

As noted above, ADRs are just like stocks. This means they trade on a stock exchange or over the counter, making them fairly easy to access and trade. Investors can also easily track their performance by reviewing market data.

Purchasing ADRs is easy because they’re available directly through American brokers. This eliminates the need to go through foreign channels to buy stock in a company in which you may be interested. Since they’re available domestically, shares are denominated in U.S. dollars. But that doesn’t mean you avoid any direct risks associated with fluctuations in currency rates.

One of the most obvious benefits of investing in ADRs is that they provide investors with a way to diversify their portfolios. Investing in international securities allows you to open your investment portfolio up to greater rewards (along with the risks).

Disadvantages

The main problems associated with ADRs are that they may involve double taxation—locally and abroad—and how many companies are listed. Unlike domestic companies, there are a limited number of foreign entities whose ADRs are listed for the public to trade.

As noted above, some ADRs may not comply with SEC regulations. These are called unsponsored ADRs, which have no direct involvement by the company. In fact, some companies may not even provide permission to list their shares this way.

Although investors can avoid any of the direct risks that come with currency exchange, they may incur currency conversion fees when they invest in ADRs. These fees are established in order to directly link the foreign security and the one traded on the domestic market.

History of American Depositary Receipts

Before American depositary receipts were introduced in the 1920s, American investors who wanted shares of a non-U.S. listed company could only do so on international exchanges—an unrealistic option for the average person back then.

While easier in the contemporary digital age, there are still drawbacks to purchasing shares on international exchanges. One particularly daunting roadblock is currency exchange issues. Another important drawback is the regulatory differences between U.S. and foreign exchanges.

Before investing in an internationally traded company, U.S. investors have to familiarize themselves with the different financial authority’s regulations, or they could risk misunderstanding important information, such as the company’s financials. They might also need to set up a foreign account, as not all domestic brokers can trade internationally.

ADRs were developed because of the complexities involved in buying shares in foreign countries and the difficulties associated with trading at different prices and currency values. J.P. Morgan’s (JPM) predecessor firm Guaranty Trust pioneered the ADR concept. In 1927, it created and launched the first ADR, enabling U.S. investors to buy shares of famous British retailer Selfridges and helping the luxury depart store tap into global markets. The ADR was listed on the New York Curb Exchange.

A few years later, in 1931, the bank introduced the first sponsored ADR for British music company Electrical & Musical Industries (also known as EMI), the eventual home of the Beatles. Today, J.P. Morgan and BNY Mellon, another U.S. bank, continue to be actively involved in the ADR markets.

Real-World Example of ADRs

Between 1988 and 2018, German car manufacturer Volkswagen AG traded OTC in the U.S. as a sponsored ADR under the ticker VLKAY. In August 2018, Volkswagen terminated its ADR program. The next day, J.P. Morgan established an unsponsored ADR for Volkswagen, now trading under the ticker VWAGY.

Investors who held the old VLKAY ADRs had the option of cashing out, exchanging the ADRs for actual shares of Volkswagen stock—trading on German exchanges—or exchanging them for the new VWAGY ADRs.

The Bottom Line

American Depositary Receipts, or ADRs, allow Americans to invest in foreign companies. Although these companies do not ordinarily trade on the U.S. stock market, an ADR allows an investor to buy these stocks as easily as they would invest in any domestic stock. The arrangement also benefits foreign firms, allowing them to raise capital from the U.S. market.

Correction—Jan. 24, 2023: A previous version of this article wrongly stated that foreign currency exchange rate fluctuations do not affect the price of ADR and therefore ADR holders avoid any direct risks associated with fluctuations in currency rates. Actually, ADR have exchange rate risk and the price of an ADR is affected by the movements of both the company’s local share price and the national currency rate of exchange against the U.S. dollar.