What Is an Autoregressive Model?

A statistical model is autoregressive if it predicts future values based on past values. For example, an autoregressive model might seek to predict a stock’s future prices based on its past performance.

Understanding Autoregressive Models

Autoregressive models operate under the premise that past values have an effect on current values, which makes the statistical technique popular for analyzing nature, economics, and other processes that vary over time. Multiple regression models forecast a variable using a linear combination of predictors, whereas autoregressive models use a combination of past values of the variable.

An AR(1) autoregressive process is one in which the current value is based on the immediately preceding value, while an AR(2) process is one in which the current value is based on the previous two values. An AR(0) process is used for white noise and has no dependence between the terms. In addition to these variations, there are also many different ways to calculate the coefficients used in these calculations, such as the least squares method.

These concepts and techniques are used by technical analysts to forecast security prices. However, since autoregressive models base their predictions only on past information, they implicitly assume that the fundamental forces that influenced the past prices will not change over time. This can lead to surprising and inaccurate predictions if the underlying forces in question are in fact changing, such as if an industry is undergoing rapid and unprecedented technological transformation.

Nevertheless, traders continue to refine the use of autoregressive models for forecasting purposes. A great example is the Autoregressive Integrated Moving Average (ARIMA), a sophisticated autoregressive model that can take into account trends, cycles, seasonality, errors, and other non-static types of data when making forecasts.

Example of an Autoregressive Model

Autoregressive models are based on the assumption that past values have an effect on current values. For example, an investor using an autoregressive model to forecast stock prices would need to assume that new buyers and sellers of that stock are influenced by recent market transactions when deciding how much to offer or accept for the security.

Although this assumption will hold under most circumstances, this is not always the case. For example, in the years prior to the 2008 Financial Crisis, most investors were not aware of the risks posed by the large portfolios of mortgage-backed securities held by many financial firms. During those times, an investor using an autoregressive model to predict the performance of U.S. financial stocks would have had good reason to predict an ongoing trend of stable or rising stock prices in that sector. 

However, once it became public knowledge that many financial institutions were at risk of imminent collapse, investors suddenly became less concerned with these stocks’ recent prices and far more concerned with their underlying risk exposure. Therefore, the market rapidly revalued financial stocks to a much lower level, a move which would have utterly confounded an autoregressive model.

It is important to note that, in an autoregressive model, a one-time shock will affect the values of the calculated variables infinitely into the future. Therefore, the legacy of the financial crisis lives on in today’s autoregressive models.

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What Is an American Depositary Share (ADS)?

An American depositary share (ADS) is an equity share of a non-U.S. company that is held by a U.S. depositary bank and is available for purchase by U.S. investors.

The entire issuance of shares by a foreign company is called an American Depositary Receipt (ADR), while the individual shares are referred to as ADSs. But the terms American Depositary Shares and American Depositary Receipts are often used interchangeably.

Understanding American Depositary Shares

An ADR is a negotiable certificate issued by a U.S. bank, under agreement with the foreign company, and is evidence of ownership of ADSs, much the same way a stock certificate denotes ownership of equity shares.

ADSs are meant to facilitate trading of the shares. They can trade over-the-counter (OTC) or on a major exchange such as the New York Stock Exchange (NYSE) or the Nasdaq (Nasdaq), depending on how much the foreign company is willing to comply with U.S. regulations. Listing on a major exchange generally requires the same level of reporting as that done by domestic companies, as well as adherence to Generally Accepted Accounting Principles (GAAP).

The Benefits of ADSs

Foreign companies that choose to offer shares on U.S. exchanges gain the advantage of a wider investor base, which can also lower costs of future capital. For U.S. investors, ADSs offer the opportunity to invest in foreign companies without dealing with currency conversions and other cross-border administrative hoops.

The Downside of ADSs

There is some currency risk involved in holding ADSs. Fluctuations in the exchange rate between the U.S. dollar and the foreign currency will have some effect on the price of shares as well as on any income payments, which must be converted into U.S. dollars.

Tax treatment of dividends from ADSs is also different. Most countries apply a withholding amount on dividends issued for ADRs. This withholding amount can vary. For example, Chile and Switzerland withhold 35% while France can withhold as much as 75% of the tax on dividends, in the case of non-cooperative countries within the EU. The withholding tax is in addition to the dividend tax already levied by U.S. authorities. The dividend tax can be avoided by ADR investors by filling out Form 1116 for foreign tax credit.

Real World Examples of ADSs

A single ADS often represents more than one share of common stock. Further, ADSs can “gap” up or down outside of U.S. trading hours, when trading is happening in the company’s home country and U.S. markets are closed.

For example, South Korea’s Woori Bank, a subsidiary of Woori Financial Group, has ADSs that are traded in the U.S. The bank’s ADS gapped up by $0.03 on July 20, 2016. A technical analysis of the price action on this ADS shows that for the past decade, its price continued higher two-thirds of the time after a gap up.

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.

What Is an Accredited Investor?

An accredited investor is an individual or a business entity that is allowed to trade securities that may not be registered with financial authorities. They are entitled to this privileged access by satisfying at least one requirement regarding their income, net worth, asset size, governance status, or professional experience.

In the U.S., the term accredited investor is used by the Securities and Exchange Commission (SEC) under Regulation D to refer to investors who are financially sophisticated and have a reduced need for the protection provided by regulatory disclosure filings. Accredited investors include high-net-worth individuals (HNWIs), banks, insurance companies, brokers, and trusts.

Understanding Accredited Investors

Accredited investors are legally authorized to purchase securities that are not registered with regulatory authorities like the SEC. Many companies decide to offer securities to this class of accredited investors directly. Because this decision allows companies exemption from registering securities with the SEC, it can save them a lot of money.

This type of share offering is referred to as a private placement. It has the potential to present these accredited investors with a great deal of risk. Therefore authorities need to ensure that they are financially stable, experienced, and knowledgeable about their risky ventures.

When companies decide to offer their shares to accredited investors, the role of regulatory authorities is limited to verifying or offering the necessary guidelines for setting benchmarks to determine who qualifies as an accredited investor. Regulatory authorities help determine if the applicant possesses the necessary financial means and knowledge to take the risks involved in investing in unregistered securities.

Accredited investors also have privileged access to venture capital, hedge funds, angel investments, and deals involving complex and higher-risk investments and instruments.

Requirements for Accredited Investors

The regulations for accredited investors vary from one jurisdiction to the other and are often defined by a local market regulator or a competent authority. In the U.S, the definition of an accredited investor is put forth by SEC in Rule 501 of Regulation D.

To be an accredited investor, a person must have an annual income exceeding $200,000 ($300,000 for joint income) for the last two years with the expectation of earning the same or a higher income in the current year. An individual must have earned income above the thresholds either alone or with a spouse over the last two years. The income test cannot be satisfied by showing one year of an individual’s income and the next two years of joint income with a spouse.

A person is also considered an accredited investor if they have a net worth exceeding $1 million, either individually or jointly with their spouse. This amount cannot include a primary residence. The SEC also considers a person to be an accredited investor if they are a general partner, executive officer, or director for the company that is issuing the unregistered securities.

An entity is considered an accredited investor if it is a private business development company or an organization with assets exceeding $5 million. Also, if an entity consists of equity owners who are accredited investors, the entity itself is an accredited investor. However, an organization cannot be formed with the sole purpose of purchasing specific securities.

Recent Changes to the Accredited Investor Definition

Recently, the U.S. Congress modified the definition of an accredited investor to include registered brokers and investment advisors.

On Aug. 26, 2020, the U.S. Securities and Exchange Commission amended the definition of an accredited investor. According to the SEC’s press release, “the amendments allow investors to qualify as accredited investors based on defined measures of professional knowledge, experience or certifications in addition to the existing tests for income or net worth. The amendments also expand the list of entities that may qualify as accredited investors, including by allowing any entity that meets an investments test to qualify.”

Among other categories, the SEC now defines accredited investors to include the following: individuals who have certain professional certifications, designations, or credentials; individuals who are “knowledgeable employees” of a private fund; and SEC- and state-registered investment advisors.

Purpose of Accredited Investor Requirements 

Any regulatory authority of a market is tasked with both promoting investment and safeguarding investors. On one hand, regulators have a vested interest in promoting investments in risky ventures and entrepreneurial activities because they have the potential to emerge as multi-baggers in the future. Such initiatives are risky, may be focused on concept-only research and development activities without any marketable product, and may have a high chance of failure. If these ventures are successful, they offer a big return to their investors. However, they also have a high probability of failure.

On the other hand, regulators need to protect less-knowledgeable, individual investors who may not have the financial cushion to absorb high losses or understand the risks associated with their investments. Therefore, the provision of accredited investors allows access for both investors who are financially well-equipped, as well as investors who are knowledgeable and experienced.

There is no formal process for becoming an accredited investor. Rather, it is the responsibility of the sellers of such securities to take a number of different steps in order to verify the status of entities or individuals who wish to be treated as accredited investors. 

Individuals or parties who want to be accredited investors can approach the issuer of the unregistered securities. The issuer may ask the applicant to respond to a questionnaire to determine if the applicant qualifies as an accredited investor. The questionnaire may require various attachments: account information, financial statements, and a balance sheet to verify the qualification. The list of attachments can extend to tax returns, W-2 forms, salary slips, and even letters from reviews by CPAs, tax attorneys, investment brokers, or advisors. Additionally, the issuers may also evaluate an individual’s credit report for additional assessment.

Example of an Accredited Investor

For example, suppose there is an individual whose income was $150,000 for the last three years. They reported a primary residence value of $1 million (with a mortgage of $200,000), a car worth $100,000 (with an outstanding loan of $50,000), a 401(k) account with $500,000, and a savings account with $450,000. While this individual fails the income test, they are an accredited investor according to the test on net worth, which cannot include the value of an individual’s primary residence. Net worth is calculated as assets minus liabilities.

This person’s net worth is exactly $1 million. This involves a calculation of their assets (other than their primary residence) of $1,050,000 ($100,000 + $500,000 + $450,000) less a car loan equaling $50,000. Since they meet the net worth requirement, they qualify to be an accredited investor.

The Bottom Line

The accredited investor rules are designed to protect potential investors with limited financial knowledge from risky ventures and losses they may be ill equipped to withstand. But on the flip side, it gives people already starting off with large financial assets a major advantage over those with more modest assets.