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 Anti-Dilution Provision?

Anti-dilution provisions are clauses built into convertible preferred stocks and some options to help shield investors from their investment potentially losing value. When new issues of a stock hit the market at a cheaper price than that paid by earlier investors in the same stock, then equity dilution can occur. Anti-dilution provisions are also referred to as anti-dilution clauses, subscription rights, subscription privileges, or preemptive rights.

Understanding Anti-Dilution Provisions

Anti-dilution provisions act as a buffer to protect investors against their equity ownership positions becoming diluted or less valuable. This can happen when the percentage of an owner’s stake in a company decreases because of an increase in the total number of shares outstanding. Total shares outstanding may increase because of new share issuance based on a round of equity financing. Dilution can also occur when holders of stock options, such as company employees, or holders of other optionable securities exercise their options.

Sometimes the company receives enough cash in exchange for the shares that the increase in the value of the shares offsets the effects of dilution; but often this is not the case.

Anti-Dilution Provisions at Work

Dilution can be particularly vexing to preferred shareholders of venture capital deals, whose stock ownership may become diluted when later issues of the same stock hit the market at a cheaper price. Anti-dilution provisions can discourage this from happening by tweaking the conversion price between convertible securities, such as corporate bonds or preferred shares, and common stocks. In this way, anti-dilution clauses can keep an investor’s original ownership percentage intact.

Dilution in Action

• As a simple example of dilution, assume that an investor owns 200,000 shares of a company that has 1,000,000 shares outstanding. The price per share is $5, meaning that the investor has a $1,000,000 stake in a company valued at $5,000,000. The investor owns 20% of the company.
• Next, assume that the company enters a new round of financing and issues 1,000,000 more shares, bringing the total shares outstanding to 2,000,000. Now, at that same $5 per share price, the investor owns a $1,000,000 stake in a $10,000,000 company. Instantly, the investors’ ownership has been diluted to 10%.

Types of Anti-Dilution Provisions

The two common types of anti-dilution clauses are known as “full ratchet” and “weighted average.”

With a full ratchet provision, the conversion price of the existing preferred shares is adjusted downward to the price at which new shares are issued in later rounds. Very simply, if the original conversion price was $5 and in a later round the conversion price is $2.50, the investor’s original conversion price would adjust to $2.50.

The weighted average provision uses the following formula to determine new conversion prices:

• C2 = C1 x (A + B) / (A + C)

Where:

• C2 = new conversion price
• C1 = old conversion price
• A = number of outstanding shares before a new issue
• B = total consideration received by the company for the new issue
• C = number of new shares issued

What Is the Arms Index (TRIN)?

The Arms Index, also called the Short-Term Trading Index (TRIN) is a technical analysis indicator that compares the number of advancing and declining stocks (AD Ratio) to advancing and declining volume (AD volume). It is used to gauge overall market sentiment. Richard W. Arms, Jr. invented it in 1967, and it measures the relationship between market supply and demand. It serves as a predictor of future price movements in the market, primarily on an intraday basis. It does this by generating overbought and oversold levels, which indicate when the index (and the majority of stocks in it) will change direction.

The Formula for Arms Index (TRIN) is:


$\begin{aligned} &\text{TRIN}\ =\ \frac{\text{Advancing Stocks/Declining Stocks}}{\text{Advancing Volume/Declining Volume}}\\ &\textbf{where:}\\ & \begin{aligned} \text{Advancing Stocks}\ =\ &\text{Number of stocks that are higher}\\ &\text{on the day}\end{aligned}\\ &\begin{aligned} \text{Declining Stocks}\ =\ &\text{Number of stocks that are lower}\\ &\text{on the day}\end{aligned}\\ &\begin{aligned} \text{Advancing Volume}\ =\ &\text{Total volume of all advancing}\\ &\text{stocks}\end{aligned}\\ &\begin{aligned}\text{Declining Volume}\ =\ &\text{Total volume of all declining}\\ &\text{stocks}\end{aligned} \end{aligned}$​TRIN = Advancing Volume/Declining VolumeAdvancing Stocks/Declining Stocks​where:Advancing Stocks = ​Number of stocks that are higher​Declining Stocks = ​Number of stocks that are lower​Advancing Volume = ​Total volume of all advancing​​

How to Calculate the Arms Index (TRIN)

TRIN is provided in many charting applications. To calculate by hand, use the following steps.

1. At set intervals, such as every five minutes or daily (or whatever interval is chosen), find the AD Ratio by dividing the number of advancing stocks by the number of declining stocks.
2. Divide total advancing volume by total declining volume to get AD Volume.
3. Divide the AD Ratio by AD Volume.
4. Record the result and plot on a graph.
5. Repeat the calculation at the next chosen time interval.
6. Connect multiple data points to form a graph and see how the TRIN moves over time.

What Does the Arms Index (TRIN) Tell You?

The Arms index seeks to provide a more dynamic explanation of overall movements in the composite value of stock exchanges, such as the NYSE or NASDAQ, by analyzing the strength and breadth of these movements.

An index value of 1.0 indicates that the ratio of AD Volume is equal to the AD Ratio. The market is said to be in a neutral state when the index equals 1.0, since the up volume is evenly distributed over the advancing issues and the down volume is evenly distributed over the declining issues.

Many analysts believe that the Arms Index provides a bullish signal when it’s less than 1.0, since there’s greater volume in the average up stock than the average down stock. In fact, some analysts have found that the long-term equilibrium for the index is below 1.0, potentially confirming that there is a bullish bias to the stock market.

On the other hand, a reading of greater than 1.0 is typically seen as a bearish signal, since there’s greater volume in the average down stock than the average up stock.

The farther away from 1.00 the Arms Index value is, the greater the contrast between buying and selling on that day. A value that exceeds 3.00 indicates an oversold market and that bearish sentiment is too dramatic. This could mean an upward reversal in prices/index is coming.

Conversely, a TRIN value that dips below 0.50 may indicate an overbought market and that bullish sentiment is overheating.

Traders look not only at the value of the indicator but also at how it changes throughout the day. They look for extremes in the index value for signs that the market may soon change directions.

The Difference Between the Arms Index (TRIN) and the Tick Index (TICK)

TRIN compares the number of advancing and declining stocks to the volume in both advancing and declining stocks. The Tick index compares the number of stocks making an uptick to the number of stocks making a downtick. The Tick Index is used to gauge intraday sentiment. The Tick Index does not factor volume, but extreme readings still signal potentially overbought or oversold conditions.

Limitations of Using the Arms Index (TRIN)

The Arms Index has a few mathematical peculiarities that traders and investors should be aware of when using it. Since the index emphasizes volume, inaccuracies arise when there isn’t as much advancing volume in advancing issues as expected. This may not be a typical situation, but it’s a situation that can arise and could potentially make the indicator unreliable.

Here are two examples of instances where problems may occur:

• Suppose that a very bullish day occurs where there are twice as many advancing issues as declining issues and twice as much advancing volume as declining volume. Despite the very bullish trading, the Arms Index would yield only a neutral value of (2/1)/(2/1) = 1.0, suggesting that the index’s reading may not be entirely accurate.
• Suppose that another bullish scenario occurs where there are three times as many advancing issues as declining issues and twice as much advancing volume than declining volume. In this case, the Arms Index would actually yield a bearish (3/1)/(2/1) = 1.5 reading, again suggesting an inaccuracy.

One way to solve this problem would be to separate the two components of the indicator into issues and volume instead of using them in the same equation. For instance, advancing issues divided by declining issues could show one trend, while advancing volume over declining volume could show a separate trend. These ratios are called the advance/decline ratio and upside/downside ratio, respectively. Both of these could be compared to tell the market’s true story.

What Is Asset Allocation?

Asset allocation is an investment strategy that aims to balance risk and reward by apportioning a portfolio’s assets according to an individual’s goals, risk tolerance, and investment horizon. The three main asset classes—equities, fixed-income, and cash and equivalents—have different levels of risk and return, so each will behave differently over time.

Why Asset Allocation Is Important

There is no simple formula that can find the right asset allocation for every individual. However, the consensus among most financial professionals is that asset allocation is one of the most important decisions that investors make. In other words, the selection of individual securities is secondary to the way that assets are allocated in stocks, bonds, and cash and equivalents, which will be the principal determinants of your investment results.

Investors may use different asset allocations for different objectives. Someone who is saving for a new car in the next year, for example, might invest their car savings fund in a very conservative mix of cash, certificates of deposit (CDs), and short-term bonds. An individual who is saving for retirement that may be decades away typically invests the majority of their individual retirement account (IRA) in stocks, since they have a lot of time to ride out the market’s short-term fluctuations. Risk tolerance plays a key factor as well. Someone who is uncomfortable investing in stocks may put their money in a more conservative allocation despite a long-term investment horizon.

Age-Based Asset Allocation

In general, stocks are recommended for holding periods of five years or longer. Cash and money market accounts are appropriate for objectives less than a year away. Bonds fall somewhere in between. In the past, financial advisors have recommended subtracting an investor’s age from 100 to determine what percentage should be invested in stocks. For example, a 40-year-old would be 60% invested in stocks. Variations of the rule recommend subtracting age from 110 or 120, given that the average life expectancy continues to grow. As individuals approach retirement age, portfolios should generally move to a more conservative asset allocation to help protect assets.

Achieving Asset Allocation Through Life-Cycle Funds

Asset-allocation mutual funds, also known as life-cycle, or target-date, funds, are an attempt to provide investors with portfolio structures that address an investor’s age, risk appetite, and investment objectives with an appropriate apportionment of asset classes. However, critics of this approach point out that arriving at a standardized solution for allocating portfolio assets is problematic because individual investors require individual solutions.

The Vanguard Target Retirement 2030 Fund would be an example of a target-date fund. These funds gradually reduce the risk in their portfolios as they near the target date, cutting riskier stocks and adding safer bonds in order to preserve the nest egg. The Vanguard 2030 fund, set up for people expecting to retire between 2028 and 2032, had a 65% stock/35% bond allocation as of Jan. 31, 2022. As 2030 approaches, the fund will gradually shift to a more conservative mix, reflecting the individual’s need for more capital preservation and less risk.

Bottom Line

Most financial professionals will tell you that asset allocation is one of the most important decisions that investors make. In other words, the selection of individual securities is secondary to the way that assets are allocated in stocks, bonds, and cash and equivalents, which will be the principal determinants of your investment results.