Diffusion Index: Overview, Formula, Limitations

What Is a Diffusion Index?

Used in technical analysis, a diffusion index measures the number of stocks that have advanced in price or are showing positive momentum. It is useful for determining the underlying strength of the stock market overall, as lots of stocks advancing show a strong market, while few(er) stocks advancing show a weaker market. In the stock market, the diffusion index is usually measured from day to day. Advancing stocks are those that moved up from the prior closing price.

A diffusion index also refers to how many Business Cycle Indicators (BCI) are moving together. This is useful for assessing the strength of the economy. "Diffusion index" is a general term that may be used in other areas of statistics or finance to assess how many components of a group are moving higher or lower.

Diffusion Index Formula

 $\begin{aligned} &\text{Diffusion Index (DI)} = ( \text{Advances} - \text{Declines} ) + \text{PDIV} \\ &\textbf{where:}\\ &\text{Advances} = \text{Number of stocks moving higher} \\ &\text{Declines} = \text{Number of stocks moving lower} \\ &\text{PDIV} = \text{Previous DI value} \\ \end{aligned}$​Diffusion Index (DI)=(Advances−Declines)+PDIVwhere:Advances=Number of stocks moving higherDeclines=Number of stocks moving lowerPDIV=Previous DI value​

Understanding the Diffusion Index

The diffusion index, also known as the advance/decline index, is one of many different forecasting tools used by technical analysts to signal when the market is bullish or bearish. The diffusion index is a breadth indicator. Breadth indicators measure how many stocks are participating in a rise or fall in the stock market.

Generally, if the diffusion index is rising with a stock index, that helps confirm that the uptrend within the stock index is strong, as an increasing number of stocks are moving higher.

If the diffusion index starts to fall while the stock index is still rising, this is called bearish divergence. It means fewer stocks are participating in the stock index rise, which is a warning sign that the stock index could eventually head lower.

If the diffusion index is falling as the stock index falls, that helps confirm the downtrend. It means fewer stocks are advancing, which makes sense since the stock index is declining (and the stocks within the stock index are declining).

If the stock index is falling, and the diffusion index starts rising, that is called bullish divergence. It means more stocks are starting to rise, which means the stock index could start heading higher soon.

Special Considerations

The diffusion index can also help an economist or trader interpret the BCIs more accurately. This group of indicators is used to assess the economy. Since there are multiple indicators, that may all say different things, it helps to create a diffusion index to see whether the majority of the indicators point toward an improving economy or a deteriorating one.

This sort of diffusion index is calculated differently and is often expressed as a percent. Rising indicators are given a value of one, unchanged indicators are given a value of 0.5, and falling indicators are given a value of zero. Assume that out of 10 indicators we get a score of 7.5. Divide that by the number of indicators (10 in this case), and then multiply by 100 to get a percentage. In this case, 75% of the indicators signal increasing economic activity.

Diffusion Index vs. Tick Index

A diffusion index measures how many stocks are advancing within an index, typically on a daily time frame. In other words, it measures how many stocks advanced from the close of the prior session. The tick index is a shorter-term breadth indicator, as it measures how many stocks had an uptick versus a downtick. An uptick is a traded price higher than the last, and a downtick is a traded price lower than the last.

Limitation of Using a Diffusion Index

For the stock market, a diffusion index sometimes doesn't work so well on Nasdaq-related indexes. This is because small speculative Nasdaq stocks are more prone to bankruptcy or delisting than NYSE stocks. Therefore, while currently listed Nasdaq stocks may be rising, all those delisted ones keep dragging on the cumulative diffusion index. Therefore, the diffusion index may decline for a long time, during certain periods, even while the Nasdaq indexes are rising.

Diffusion index divergence is a poor trade timing signal. Divergence can last longer than many traders expect which means it may not be wise to trade on divergence as soon as it is spotted. It is better to wait for the price to confirm the divergence. For example, if bullish divergence forms, don't buy immediately. Wait for the stock index to start rising before buying.

As for applying a diffusion index to other groups of data, such as the BCIs, it is important to remember that not all data points within the group may be of equal importance. A rapidly rising indicator is only given a point value of one, while a mediocre rise is also given a value of one. The diffusion index may over-simplify the data. Therefore, it is still a good idea to look at the individual indicators and what they are saying, as well as the diffusion index.