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 Arbitrage Pricing Theory (APT)?

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset’s returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced.

The Formula for the Arbitrage Pricing Theory Model Is


$\begin{aligned} &\text{E(R)}_\text{i} = E(R)_z + (E(I) – E(R)_z) \times \beta_n\\ &\textbf{where:}\\ &\text{E(R)}_\text{i} = \text{Expected return on the asset}\\ &R_z = \text{Risk-free rate of return}\\ &\beta_n = \text{Sensitivity of the asset price to macroeconomic} \\ &\text{factor}\textit{ n}\\ &Ei = \text{Risk premium associated with factor}\textit{ i}\\ \end{aligned}$​E(R)i​=E(R)z​+(E(I)−E(R)z​)×βn​where:E(R)i​=Expected return on the assetRz​=Risk-free rate of returnβn​=Sensitivity of the asset price to macroeconomicfactor nEi=Risk premium associated with factor i​

The beta coefficients in the APT model are estimated by using linear regression. In general, historical securities returns are regressed on the factor to estimate its beta.

How the Arbitrage Pricing Theory Works

The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (CAPM). Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.

However, this is not a risk-free operation in the classic sense of arbitrage, because investors are assuming that the model is correct and making directional trades—rather than locking in risk-free profits.

Mathematical Model for the APT

While APT is more flexible than the CAPM, it is more complex. The CAPM only takes into account one factor—market risk—while the APT formula has multiple factors. And it takes a considerable amount of research to determine how sensitive a security is to various macroeconomic risks.

The factors as well as how many of them are used are subjective choices, which means investors will have varying results depending on their choice. However, four or five factors will usually explain most of a security’s return. (For more on the differences between the CAPM and APT, read more about how CAPM and arbitrage pricing theory differ.)

APT factors are the systematic risk that cannot be reduced by the diversification of an investment portfolio. The macroeconomic factors that have proven most reliable as price predictors include unexpected changes in inflation, gross national product (GNP), corporate bond spreads and shifts in the yield curve. Other commonly used factors are gross domestic product (GDP), commodities prices, market indices, and exchange rates.

Example of How Arbitrage Pricing Theory Is Used

For example, the following four factors have been identified as explaining a stock’s return and its sensitivity to each factor and the risk premium associated with each factor have been calculated:

• Gross domestic product (GDP) growth: ß = 0.6, RP = 4%
• Inflation rate: ß = 0.8, RP = 2%
• Gold prices: ß = -0.7, RP = 5%
• Standard and Poor’s 500 index return: ß = 1.3, RP = 9%
• The risk-free rate is 3%

Using the APT formula, the expected return is calculated as:

• Expected return = 3% + (0.6 x 4%) + (0.8 x 2%) + (-0.7 x 5%) + (1.3 x 9%) = 15.2%

What Is Adjusted Present Value (APV)?

The adjusted present value is the net present value (NPV) of a project or company if financed solely by equity plus the present value (PV) of any financing benefits, which are the additional effects of debt. By taking into account financing benefits, APV includes tax shields such as those provided by deductible interest.

The Formula for APV Is


$\begin{aligned} &\text{Adjusted Present Value = Unlevered Firm Value + NE}\\ &\textbf{where:}\\ &\text{NE = Net effect of debt}\\ \end{aligned}$​Adjusted Present Value = Unlevered Firm Value + NEwhere:NE = Net effect of debt​

The net effect of debt includes tax benefits that are created when the interest on a company’s debt is tax-deductible. This benefit is calculated as the interest expense times the tax rate, and it only applies to one year of interest and tax. The present value of the interest tax shield is therefore calculated as: (tax rate * debt load * interest rate) / interest rate.

How to Calculate Adjusted Present Value (APV)

To determine the adjusted present value:

1. Find the value of the un-levered firm.
2. Calculate the net value of debt financing.
3. Sum the value of the un-levered project or company and the net value of the debt financing.

How to Calculate APV in Excel

An investor can use Excel to build out a model to calculate the net present value of the firm and the present value of the debt.

What Does Adjusted Present Value Tell You?

The adjusted present value helps to show an investor the benefits of tax shields resulting from one or more tax deductions of interest payments or a subsidized loan at below-market rates. For leveraged transactions, APV is preferred. In particular, leveraged buyout situations are the most effective situations in which to use the adjusted present value methodology.

The value of a debt-financed project can be higher than just an equity-financed project, as the cost of capital falls when leverage is used. Using debt can actually turn a negative NPV project into one that’s positive. NPV uses the weighted average cost of capital as the discount rate, while APV uses the cost of equity as the discount rate.

Example of How to Use Adjusted Present Value (APV)

In a financial projection where a base-case NPV is calculated, the sum of the present value of the interest tax shield is added to obtain the adjusted present value.

For example, assume a multi-year projection calculation finds that the present value of Company ABC’s free cash flow (FCF) plus terminal value is $100,000. The tax rate for the company is 30% and the interest rate is 7%. Its $50,000 debt load has an interest tax shield of $15,000, or ($50,000 * 30% * 7%) / 7%. Thus, the adjusted present value is $115,000, or $100,000 + $15,000.

The Difference Between APV and Discounted Cash Flow (DCF)

While the adjusted present value method is similar to the discounted cash flow (DCF) methodology, adjusted present cash flow does not capture taxes or other financing effects in a weighted average cost of capital (WACC) or other adjusted discount rates. Unlike WACC used in discounted cash flow, the adjusted present value seeks to value the effects of the cost of equity and cost of debt separately. The adjusted present value isn’t as prevalent as the discounted cash flow method.

Limitations of Using Adjusted Present Value (APV)

In practice, the adjusted present value is not used as much as the discounted cash flow method. It is more of an academic calculation but is often considered to result in more accurate valuations.

Learn More About Adjusted Present Value (APV)

To dig deeper into calculating the adjusted present value, check out Investopedia’s guide to calculating net present value.

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.