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 an Assignment?

Assignment most often refers to one of two definitions in the financial world:

1. The transfer of an individual’s rights or property to another person or business. This concept exists in a variety of business transactions and is often spelled out contractually.
2. In trading, assignment occurs when an option contract is exercised. The owner of the contract exercises the contract and assigns the option writer to an obligation to complete the requirements of the contract.

Property Rights Assignment

Assignment refers to the transfer of some or all property rights and obligations associated with an asset, property, contract, etc. to another entity through a written agreement. For example, a payee assigns rights for collecting note payments to a bank. A trademark owner transfers, sells, or gives another person interest in the trademark. A homeowner who sells their house assigns the deed to the new buyer.

To be effective, an assignment must involve parties with legal capacity, consideration, consent, and legality of object.

Examples

A wage assignment is a forced payment of an obligation by automatic withholding from an employee’s pay. Courts issue wage assignments for people late with child or spousal support, taxes, loans, or other obligations. Money is automatically subtracted from a worker’s paycheck without consent if they have a history of nonpayment. For example, a person delinquent on $100 monthly loan payments has a wage assignment deducting the money from their paycheck and sent to the lender. Wage assignments are helpful in paying back long-term debts.

Another instance can be found in a mortgage assignment. This is where a mortgage deed gives a lender interest in a mortgaged property in return for payments received. Lenders often sell mortgages to third parties, such as other lenders. A mortgage assignment document clarifies the assignment of contract and instructs the borrower in making future mortgage payments, and potentially modifies the mortgage terms.

A final example involves a lease assignment. This benefits a relocating tenant wanting to end a lease early or a landlord looking for rent payments to pay creditors. Once the new tenant signs the lease, taking over responsibility for rent payments and other obligations, the previous tenant is released from those responsibilities. In a separate lease assignment, a landlord agrees to pay a creditor through an assignment of rent due under rental property leases. The agreement is used to pay a mortgage lender if the landlord defaults on the loan or files for bankruptcy. Any rental income would then be paid directly to the lender.

Options Assignment

Options can be assigned when a buyer decides to exercise their right to buy (or sell) stock at a particular strike price. The corresponding seller of the option is not determined when a buyer opens an option trade, but only at the time that an option holder decides to exercise their right to buy stock. So an option seller with open positions is matched with the exercising buyer via automated lottery. The randomly selected seller is then assigned to fulfill the buyer’s rights. This is known as an option assignment.

Once assigned, the writer (seller) of the option will have the obligation to sell (if a call option) or buy (if a put option) the designated number of shares of stock at the agreed-upon price (the strike price). For instance, if the writer sold calls they would be obligated to sell the stock, and the process is often referred to as having the stock called away. For puts, the buyer of the option sells stock (puts stock shares) to the writer in the form of a short-sold position.

Example

Suppose a trader owns 100 call options on company ABC’s stock with a strike price of $10 per share. The stock is now trading at $30 and ABC is due to pay a dividend shortly. As a result, the trader exercises the options early and receives 10,000 shares of ABC paid at $10. At the same time, the other side of the long call (the short call) is assigned the contract and must deliver the shares to the long.

What Is an Audit?

The term audit usually refers to a financial statement audit. A financial audit is an objective examination and evaluation of the financial statements of an organization to make sure that the financial records are a fair and accurate representation of the transactions they claim to represent. The audit can be conducted internally by employees of the organization or externally by an outside Certified Public Accountant (CPA) firm.

Understanding Audits

Almost all companies receive a yearly audit of their financial statements, such as the income statement, balance sheet, and cash flow statement. Lenders often require the results of an external audit annually as part of their debt covenants. For some companies, audits are a legal requirement due to the compelling incentives to intentionally misstate financial information in an attempt to commit fraud. As a result of the Sarbanes-Oxley Act (SOX) of 2002, publicly traded companies must also receive an evaluation of the effectiveness of their internal controls.

Standards for external audits performed in the United States, called the generally accepted auditing standards (GAAS), are set out by Auditing Standards Board (ASB) of the American Institute of Certified Public Accountants (AICPA). Additional rules for the audits of publicly traded companies are made by the Public Company Accounting Oversight Board (PCAOB), which was established as a result of SOX in 2002. A separate set of international standards, called the International Standards on Auditing (ISA), were set up by the International Auditing and Assurance Standards Board (IAASB).

Types of Audits

External Audits

Audits performed by outside parties can be extremely helpful in removing any bias in reviewing the state of a company’s financials. Financial audits seek to identify if there are any material misstatements in the financial statements. An unqualified, or clean, auditor’s opinion provides financial statement users with confidence that the financials are both accurate and complete. External audits, therefore, allow stakeholders to make better, more informed decisions related to the company being audited.

External auditors follow a set of standards different from that of the company or organization hiring them to do the work. The biggest difference between an internal and external audit is the concept of independence of the external auditor. When audits are performed by third parties, the resulting auditor’s opinion expressed on items being audited (a company’s financials, internal controls, or a system) can be candid and honest without it affecting daily work relationships within the company.

Internal Audits

Internal auditors are employed by the company or organization for whom they are performing an audit, and the resulting audit report is given directly to management and the board of directors. Consultant auditors, while not employed internally, use the standards of the company they are auditing as opposed to a separate set of standards. These types of auditors are used when an organization doesn’t have the in-house resources to audit certain parts of their own operations.

The results of the internal audit are used to make managerial changes and improvements to internal controls. The purpose of an internal audit is to ensure compliance with laws and regulations and to help maintain accurate and timely financial reporting and data collection. It also provides a benefit to management by identifying flaws in internal control or financial reporting prior to its review by external auditors.

Internal Revenue Service (IRS) Audits

The Internal Revenue Service (IRS) also routinely performs audits to verify the accuracy of a taxpayer’s return and specific transactions. When the IRS audits a person or company, it usually carries a negative connotation and is seen as evidence of some type of wrongdoing by the taxpayer. However, being selected for an audit is not necessarily indicative of any wrongdoing.

IRS audit selection is usually made by random statistical formulas that analyze a taxpayer’s return and compare it to similar returns. A taxpayer may also be selected for an audit if they have any dealings with another person or company who was found to have tax errors on their audit.

There are three possible IRS audit outcomes available: no change to the tax return, a change that is accepted by the taxpayer, or a change that the taxpayer disagrees with. If the change is accepted, the taxpayer may owe additional taxes or penalties. If the taxpayer disagrees, there is a process to follow that may include mediation or an appeal.

What Is the Altman Z-Score?

The Altman Z-score is the output of a credit-strength test that gauges a publicly traded manufacturing company’s likelihood of bankruptcy.

Understanding the Altman Z-Score

The Altman Z-score, a variation of the traditional z-score in statistics, is based on five financial ratios that can be calculated from data found on a company’s annual 10-K report. It uses profitability, leverage, liquidity, solvency, and activity to predict whether a company has a high probability of becoming insolvent.

NYU Stern Finance Professor Edward Altman developed the Altman Z-score formula in 1967, and it was published in 1968. Over the years, Altman has continued to reevaluate his Z-score. From 1969 until 1975, Altman looked at 86 companies in distress, then 110 from 1976 to 1995, and finally 120 from 1996 to 1999, finding that the Z-score had an accuracy of between 82% and 94%.

In 2012, he released an updated version called the Altman Z-score Plus that one can use to evaluate public and private companies, manufacturing and non-manufacturing companies, and U.S. and non-U.S. companies. One can use Altman Z-score Plus to evaluate corporate credit risk. The Altman Z-score has become a reliable measure of calculating credit risk.

How to Calculate the Altman Z-Score

One can calculate the Altman Z-score as follows:

Altman Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E

Where:

• A = working capital / total assets
• B = retained earnings / total assets
• C = earnings before interest and tax / total assets
• D = market value of equity / total liabilities
• E = sales / total assets

A score below 1.8 means it’s likely the company is headed for bankruptcy, while companies with scores above 3 are not likely to go bankrupt. Investors can use Altman Z-scores to determine whether they should buy or sell a stock if they’re concerned about the company’s underlying financial strength. Investors may consider purchasing a stock if its Altman Z-Score value is closer to 3 and selling or shorting a stock if the value is closer to 1.8.

In more recent years, however, a Z-Score closer to 0 indicates a company may be in financial trouble. In a lecture given in 2019 titled “50 Years of the Altman Score,” Professor Altman himself noted that recent data has shown that 0—not 1.8—is the figure at which investors should worry about a company’s financial strength. The two-hour lecture is available to view for free on YouTube.

2008 Financial Crisis

In 2007, the credit ratings of specific asset-related securities had been rated higher than they should have been. The Altman Z-score indicated that the companies’ risks were increasing significantly and may have been heading for bankruptcy.

Altman calculated that the median Altman Z-score of companies in 2007 was 1.81. These companies’ credit ratings were equivalent to a B. This indicated that 50% of the firms should have had lower ratings, were highly distressed and had a high probability of becoming bankrupt.

Altman’s calculations led him to believe a crisis would occur and there would be a meltdown in the credit market. He believed the crisis would stem from corporate defaults, but the meltdown, which brought about the 2008 financial crisis, began with mortgage-backed securities (MBS). However, corporations soon defaulted in 2009 at the second-highest rate in history.