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.

Investopedia does not provide tax, investment, or financial services and advice. The information is presented without consideration of the investment objectives, risk tolerance, or financial circumstances of any specific investor and might not be suitable for all investors. Investing involves risk, including the possible loss of principal.

What Is Alpha?

Alpha (α) is a term used in investing to describe an investment strategy’s ability to beat the market, or its “edge.” Alpha is thus also often referred to as “excess return” or “abnormal rate of return,” which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Alpha is often used in conjunction with beta (the Greek letter β), which measures the broad market’s overall volatility or risk, known as systematic market risk.

Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.

Understanding Alpha

Alpha is one of five popular technical investment risk ratios. The others are beta, standard deviation, R-squared, and the Sharpe ratio. These are all statistical measurements used in modern portfolio theory (MPT). All of these indicators are intended to help investors determine the risk-return profile of an investment.

Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

In other words, alpha is the return on an investment that is not a result of a general movement in the greater market. As such, an alpha of zero would indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any additional value compared to the broad market.

The concept of alpha became more popular with the advent of smart beta index funds tied to indexes like the Standard & Poor’s 500 index and the Wilshire 5000 Total Market Index. These funds attempt to enhance the performance of a portfolio that tracks a targeted subset of the market.

Despite the considerable desirability of alpha in a portfolio, many index benchmarks manage to beat asset managers the vast majority of the time. Due in part to a growing lack of faith in traditional financial advising brought about by this trend, more and more investors are switching to low-cost, passive online advisors (often called roboadvisors​) who exclusively or almost exclusively invest clients’ capital into index-tracking funds, the rationale being that if they cannot beat the market they may as well join it.

Moreover, because most “traditional” financial advisors charge a fee, when one manages a portfolio and nets an alpha of zero, it actually represents a slight net loss for the investor. For example, suppose that Jim, a financial advisor, charges 1% of a portfolio’s value for his services and that during a 12-month period Jim managed to produce an alpha of 0.75 for the portfolio of one of his clients, Frank. While Jim has indeed helped the performance of Frank’s portfolio, the fee that Jim charges is in excess of the alpha he has generated, so Frank’s portfolio has experienced a net loss. For investors, the example highlights the importance of considering fees in conjunction with performance returns and alpha.

The Efficient Market Hypothesis (EMH) postulates that market prices incorporate all available information at all times, and so securities are always properly priced (the market is efficient.) Therefore, according to the EMH, there is no way to systematically identify and take advantage of mispricings in the market because they do not exist.

If mispricings are identified, they are quickly arbitraged away and so persistent patterns of market anomalies that can be taken advantage of tend to be few and far between.

Empirical evidence comparing historical returns of active mutual funds relative to their passive benchmarks indicates that fewer than 10% of all active funds are able to earn a positive alpha over a 10-plus year time period, and this percentage falls once taxes and fees are taken into consideration. In other words, alpha is hard to come by, especially after taxes and fees.

Because beta risk can be isolated by diversifying and hedging various risks (which comes with various transaction costs), some have proposed that alpha does not really exist, but that it simply represents the compensation for taking some un-hedged risk that hadn’t been identified or was overlooked.

Seeking Investment Alpha

Alpha is commonly used to rank active mutual funds as well as all other types of investments. It is often represented as a single number (like +3.0 or -5.0), and this typically refers to a percentage measuring how the portfolio or fund performed compared to the referenced benchmark index (i.e., 3% better or 5% worse).

Deeper analysis of alpha may also include “Jensen’s alpha.” Jensen’s alpha takes into consideration the capital asset pricing model (CAPM) market theory and includes a risk-adjusted component in its calculation. Beta (or the beta coefficient) is used in the CAPM, which calculates the expected return of an asset based on its own particular beta and the expected market returns. Alpha and beta are used together by investment managers to calculate, compare, and analyze returns.

The entire investing universe offers a broad range of securities, investment products, and advisory options for investors to consider. Different market cycles also have an influence on the alpha of investments across different asset classes. This is why risk-return metrics are important to consider in conjunction with alpha.

Examples

This is illustrated in the following two historical examples for a fixed income ETF and an equity ETF:

The iShares Convertible Bond ETF (ICVT) is a fixed income investment with low risk. It tracks a customized index called the Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index. The 3-year standard deviation was 18.94%, as of Feb. 28, 2022. The year-to-date return, as of Feb. 28, 2022, was -6.67%. The Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index had a return of -13.17% over the same period. Therefore, the alpha for ICVT was -0 12% in comparison to the Bloomberg U.S. Aggregate Index and a 3-year standard deviation of 18.97%.

However, since the aggregate bond index is not the proper benchmark for ICVT (it should be the Bloomberg Convertible index), this alpha may not be as large as initially thought; and in fact, may be misattributed since convertible bonds have far riskier profiles than plain vanilla bonds.

The WisdomTree U.S. Quality Dividend Growth Fund (DGRW) is an equity investment with higher market risk that seeks to invest in dividend growth equities. Its holdings track a customized index called the WisdomTree U.S. Quality Dividend Growth Index. It had a three-year annualized standard deviation of 10.58%, higher than ICVT.

As of Feb. 28, 2022, DGRW annualized return was 18.1%, which was also higher than the S&P 500 at 16.4%, so it had an alpha of 1.7% in comparison to the S&P 500. But again, the S&P 500 may not be the correct benchmark for this ETF, since dividend-paying growth stocks are a very particular subset of the overall stock market, and may not even be inclusive of the 500 most valuable stocks in America.

Alpha Considerations

While alpha has been called the “holy grail” of investing, and as such, receives a lot of attention from investors and advisors alike, there are a couple of important considerations that one should take into account when using alpha.

1. A basic calculation of alpha subtracts the total return of an investment from a comparable benchmark in its asset category. This alpha calculation is primarily only used against a comparable asset category benchmark, as noted in the examples above. Therefore, it does not measure the outperformance of an equity ETF versus a fixed income benchmark. This alpha is also best used when comparing the performance of similar asset investments. Thus, the alpha of the equity ETF, DGRW, is not relatively comparable to the alpha of the fixed income ETF, ICVT.
2. Some references to alpha may refer to a more advanced technique. Jensen’s alpha takes into consideration CAPM theory and risk-adjusted measures by utilizing the risk-free rate and beta.

When using a generated alpha calculation it is important to understand the calculations involved. Alpha can be calculated using various different index benchmarks within an asset class. In some cases, there might not be a suitable pre-existing index, in which case advisors may use algorithms and other models to simulate an index for comparative alpha calculation purposes.

Alpha can also refer to the abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like CAPM. In this instance, a CAPM model might aim to estimate returns for investors at various points along an efficient frontier. The CAPM analysis might estimate that a portfolio should earn 10% based on the portfolio’s risk profile. If the portfolio actually earns 15%, the portfolio’s alpha would be 5.0, or +5% over what was predicted in the CAPM model.

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.

What Is an American Option?

An American option, aka an American-style option, is a version of an options contract that allows holders to exercise the option rights at any time before and including the day of expiration. It contrasts with another type of option, called the European option, that only allows execution on the day of expiration.

An American-style option allows investors to capture profit as soon as the stock price moves favorably, and to take advantage of dividend announcements as well.

How American Options Work

American options outline the timeframe when the option holder can exercise their option contract rights. These rights allow the holder to buy or sell—depending on if the option is a call or put—the underlying asset, at the set strike price on or before the predetermined expiration date. Since investors have the freedom to exercise their options at any point during the life of the contract, American-style options are more valuable than the limited European options. However, the ability to exercise early carries an added premium or cost.

The last day to exercise a weekly American option is normally on the Friday of the week in which the option contract expires. Conversely, the last day to exercise a monthly American option is normally the third Friday of the month.

The majority of exchange-traded options on single stocks are American, while options on indexes tend to be European style.

American Call and Put Options

A long call option gives the holder the right to demand delivery of the underlying security or stock on any day within the contract period. This feature includes any day leading up to and the day of expiration. As with all options, the buyer does not have an obligation to receive the shares and is not required to exercise their right. The strike price remains the same specified value throughout the contract.

If an investor purchased a call option for a company in March with an expiration date at the end of December of the same year, they would have the right to exercise the call option at any time up until its expiration date.

American put options also allow the execution at any point up to and including the expiration date. This ability gives the buyer the freedom to demand the seller takes delivery of the underlying asset whenever the price falls below the specified strike price.

One reason for the early exercise has to do with the cost of carry or the opportunity cost associated with not investing the gains from the put option. When a put is exercised, investors are paid the strike price immediately. As a result, the proceeds can be invested in another security to earn interest.

However, the drawback to exercising puts is that the investor would miss out on any dividends since exercising would sell the shares. Also, the option itself might continue to increase in value if held to expiry, and exercising early might lead to missing out on any further gains.

When to Exercise Early

In many instances, holders of American-style options do not utilize the early exercise provision, since it’s usually more cost-effective to either hold the contract until expiration or exit the position by selling the option contract outright. In other words, as a stock price rises, the value of a call option increases, as does its premium. Traders can sell an option back to the options market if the current premium is higher than the initial premium paid at the onset. The trader would earn the net difference between the two premiums minus any fees or commissions from the broker.

However, there are times when options are typically exercised early. Deep-in-the-money call options—where the asset’s price is well above the option’s strike price—will usually be exercised early. Puts can also be deep-in-the-money when the price is significantly below the strike price. In most cases, deep prices are those that are more than $10 in-the-money. With lower-priced equities, deep-in-the-money might be characterized as a $5 spread between the strike price and market price.

Early execution can also happen leading up to the date a stock goes ex-dividend—the cutoff date by which shareholders must own the stock to receive the next scheduled dividend payment. Option holders do not receive dividend payments. So, many investors will exercise their options before the ex-dividend date to capture the gains from a profitable position and get paid the dividend.

Advantages and Disadvantages of American Options

American options are helpful since investors don’t have to wait to exercise the option when the asset’s price rises above the strike price. However, American-style options carry a premium—an upfront cost—that investors pay and which must be factored into the overall profitability of the trade.

Examples of an American Option

Say an investor purchased an American-style call option for Apple Inc. (AAPL) in March with an expiration date at the end of December in the same year. The premium is $5 per option contract—one contract is 100 shares ($5 x 100 = $500)—and the strike price on the option is $100. Following the purchase, the stock price rose to $150 per share.

The investor exercises the call option on Apple before expiration buying 100 shares of Apple for $100 per share. In other words, the investor would be long 100 shares of Apple at the $100 strike price. The investor immediately sells the shares for the current market price of $150 and pockets the $50 per share profit. The investor earned $5,000 in total minus the premium of $500 for buying the option and any broker commission.

Let’s say an investor believes shares of Meta Inc. (META), formerly Facebook, will decline in the upcoming months. The investor purchases an American-style July put option in January, which expires in September of the same year. The option premium is $3 per contract (100 x $3 = $300) and the strike price is $150.

Meta’s stock price falls to $90 per share, and the investor exercises the put option and is short 100 shares of Meta at the $150 strike price. The transaction effectively has the investor buying 100 shares of Meta at the current $90 price and immediately selling those shares at the $150 strike price. However, in practice, the net difference is settled, and the investor earns a $60 profit on the option contract, which equates to $6,000 minus the premium of $300 and any broker commissions.

Investopedia does not provide tax, investment, or financial services and advice. The information is presented without consideration of the investment objectives, risk tolerance, or financial circumstances of any specific investor and might not be suitable for all investors. Investing involves risk, including the possible loss of principal.