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 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.

Who Is Alan Greenspan?

Alan Greenspan is an American economist who was the chair of the Board of Governors of the Federal Reserve (Fed), the United States’ central bank, from 1987 until 2006. In that role, he also served as the chair of the Federal Open Market Committee (FOMC), which is the Fed’s principal monetary policymaking committee that makes decisions on interest rates and managing the U.S. money supply.

Greenspan is best known for largely presiding over the Great Moderation, a period of relatively stable inflation and macroeconomic growth, that lasted from the mid-1980s to the financial crisis in 2007.

Early Life and Education

Alan Greenspan was born in New York City on March 6, 1926. He received his bachelor’s, master’s, and doctoral degrees in economics, all from New York University, as well as studying economics at Columbia University in the early 1950s under Arthur Burns, who would later serve two consecutive terms as chair of the Board of Governors of the Fed.

Greenspan’s first job, in 1948, was not in government but for a non-profit analyzing demand for steel, aluminum, and copper. After this, Greenspan ran an economic consulting firm in New York City, Townsend-Greenspan & Co., Inc., from 1954 to 1974 and 1977 to 1987. Greenspan began his career in the public sector in 1974 when he served as chair of the President’s Council of Economic Advisers (CEA) under President Gerald Ford.

In 1987, Greenspan became the 13th chair of the Fed, replacing Paul Volcker. President Ronald Reagan was the first to appoint Greenspan to the office, but three other presidents, George H.W. Bush, Bill Clinton, and George W. Bush, named him to four additional terms. His tenure as chair lasted for more than 18 years before he retired in 2006 to be replaced by Ben Bernanke. After leaving, he published his memoir, The Age of Turbulence, and began his own Washington DC-based consulting firm, Greenspan Associates LLC. 

Alan Greenspan was known as being adept at gaining consensus among Fed board members on policy issues and for serving during one of the most severe economic crises of the late 20th century, the aftermath of the stock market crash of 1987. After that crash, he advocated for sharply slashing interest rates to prevent the economy from sinking into a deep depression.

Alan Greenspan’s Policies and Actions

Greenspan presided over one of the most prosperous periods in American history—thanks in no small part, supporters feel, to his helming of the Fed. Still, some of his policies and actions were controversial, either at the time or in retrospect.

Views on Inflation

Early in his career, Greenspan developed a reputation for being hawkish on inflation, in part due to his advocacy for a return to the gold standard in monetary policy in the 1967 essay “Gold and Economic Freedom.” 

His allegedly “hawkish” stance was portrayed by early critics as a preference for sacrificing economic growth in exchange for preventing inflation. Greenspan eventually reversed those views as Fed chief; in a 1998 speech, he conceded that the new economy might not be as susceptible to inflation as he had first thought.

In practice, Greenspan’s supposedly hawkish approach was flexible, to say the least. He was clearly willing to risk inflation under conditions that could create a severe depression and certainly pursued a generally easy money policy relative to his predecessor, Paul Volcker. In particular, in the early 2000s, Greenspan presided over cutting interest rates to levels not seen in many decades.

Flip-Flop on Interest Rates

In 2000, Greenspan advocated reducing interest rates after the dot-com bubble burst. He did so again in 2001 after 9-11, the World Trade Center attack. Following 9-11, Greenspan led the FOMC to immediately reduce the Fed funds rate from 3.5% to 3%, and, in the following months, he worked toward lowering that rate to a record (at the time) low of 1.13% and holding it there for a full year.

Some criticized those rate cuts as having the potential to inflate asset price bubbles in the U.S. Greenspan’s pro-inflationary policies, particularly during this period, are today generally understood to have contributed to the U.S. housing bubble, subsequent subprime mortgage financial crisis, and the Great Recession, though this is of course disputed by Greenspan and his allies.

Encouraging Adjustable-Rate Mortgages

In a 2004 speech, Greenspan suggested more homeowners should consider taking out adjustable-rate mortgages (ARMs) where the interest rate adjusts itself to prevailing market interest rates. Under Greenspan’s tenure, interest rates subsequently rose as inflation accelerated. This increase reset many of those mortgages to much higher payments, creating even more distress for many homeowners and exacerbating the impact of that crisis.

The “Greenspan Put”

The “Greenspan put” was a monetary policy strategy popular during the 1990s and 2000s under Greenspan. Throughout his reign, he attempted to help support the U.S. economy by actively using the federal funds rate to aggressively lower interest rates to fight the deflation of asset price bubbles.

The Greenspan put created a substantial moral hazard in financial markets. Informed investors could expect the Fed to take predictable actions that would bailout investor’s losses, which distort the incentives of market participants. This created an environment where investors were encouraged to take excessive risk because Fed monetary policy tended to inherently limit their potential losses in the event of a market downturn in an analogous way to buying put options on the open market.

The Bottom Line

Like many other government officials, the success of Alan Greenspan’s five terms as Chair of the Fed will depend on who you ask. However, it is certainly true that Greenspan faced some massive challenges during his tenure, such as the 1987 stock market crash and the attacks on the World Trade Center.

Overall, Greenspan helped usher in a strong U.S. economy in the 1990s. Opinion on how much his actions caused the economic recession that began shortly after his term ended varies.

What Is an Allotment?

The term allotment refers to the systematic distribution or assignment of resources in a business to various entities over time. Allotment generally means the distribution of equity, particularly shares granted to a participating underwriting firm during an initial public offering (IPO).

There are several types of allotment that arise when new shares are issued and allocated to either new or existing shareholders. Companies allot shares and other resources when demand is much stronger than the available supply.

Understanding Allotments

In business, allotment describes the systematic distribution of resources across different entities and over time. In finance, the term typically relates to the allocation of shares during a public share issuance. When a private company wants to raise capital for any reason (to fund operations, make a large purchase, or acquire a rival), it may decide to issue shares by going public. Two or more financial institutions usually underwrite a public offering. Each underwriter receives a specific number of shares to sell.

The allotment process can get somewhat complicated during an IPO, even for individual investors. That’s because stock markets are incredibly efficient mechanisms for matching prices and quantities, but the demand must be estimated before an IPO takes place. Investors must express interest in how many shares they would like to purchase at a specific price before the IPO.

If demand is too high, the actual allotment of shares received by an investor may be lower than the amount requested. If demand is too low, which means the IPO is undersubscribed, then the investor may be able to get the desired allotment at a lower price.

On the other hand, low demand often leads to the share price falling after the IPO takes place. This means that the allotment is oversubscribed.

Other Forms of Allotment

An IPO is not the only case of share allocation. Allotment can also occur when a company’s directors earmark new shares to predetermined shareholders. These are investors who have either applied for new shares or earned them by owning existing shares. For example, the company allocates shares proportionately based on existing ownership in a stock split.

Companies allot shares to their employees through employee stock options (ESOs). This is a form of compensation that companies offer to attract new and keep existing employees in addition to salaries and wages. ESOs incentivize employees to perform better by increasing the number of shares without diluting ownership.

Rights offerings or rights issues allocate shares to investors who wish to purchase more rather than doing so automatically. Thus, it gives investors the right but not the obligation to purchase additional shares in the company. Some companies may elect to do a rights issue to the shareholders of a company they want to acquire. This allows the acquiring company to raise capital by giving investors in the target firm an ownership stake in the newly formed company.

Reasons for Raising Shares

The number one reason a company issues new shares for allotment is to raise money to finance business operations. An IPO is also used to raise capital. In fact, there are very few other reasons why a company would issue and allocate new shares.

New shares can be issued to repay a public company’s short- or long-term debt. Paying down debt helps a company with interest payments. It also changes critical financial ratios such as the debt-to-equity ratio and debt-to-asset ratio. There are times when a company may want to issue new shares, even if there is little or no debt. When companies face situations where current growth is outpacing sustainable growth, they may issue new shares to fund the continuation of organic growth.

Company directors may issue new shares to fund the acquisition or takeover of another business. In the case of a takeover, new shares can be allotted to existing shareholders of the acquired company, efficiently exchanging their shares for equity in the acquiring company.

As a form of reward to existing shareholders and stakeholders, companies issue and allot new shares. A scrip dividend, for example, is a dividend that gives equity holders some new shares proportional to the value of what they would have received had the dividend been cash.

Overallotment Options

There are options for underwriters where additional shares can be sold in an IPO or follow-on offering. This is called an overallotment or greenshoe option.

In an overallotment, underwriters have the option to issue more than 15% shares than the company originally intended to do. This option doesn’t have to be exercised the day of the overallotment. Instead, companies can take as long as 30 days to do so. Companies do this when shares trade higher than the offering price and when demand is really high.

Overallotments allow companies to stabilize the price of their shares on the stock market while ensuring it floats below the offering price. If the price increases above this threshold, underwriters can purchase the additional shares at the offering price. Doing so ensures they don’t have to deal with losses. But if the price falls below the offering price, underwriters can decrease the supply by purchasing some of the shares. This may push the price up.