# Directional Index

Directional Index or DI is used to analyze the trend of a stock or a commodity. It is part of The Directional Movement System, developed by J.Welles Wilder. It was developed in 1978. Since then it is widely used in stock trading for the technical analysis of the stock.

The Directional Movement System comprises of five indicators namely:

All these are thoroughly explained in the book, New Concepts in Technical Trading Systems (Click here to buy this book ) written by J.Welles Wilder. This book gives complete instructions on calculating and interpreting each of the above indicators along with examples.

Welles Wilder is very fascinated about Directional Movement System. He is also very proud of it. He says it is one of his most satisfying achievements, when he could actually able to reduce this concept to an absolute mathematical equation.

Directional Index or DI is developed as an indicator to determine the trend in a series of prices of a financial instrument. It has become a widely used indicator for technical analysts, and is provided as a standard in collections of indicators offered by various stock technical analysis software and trading platforms.

Construction
First the absolute up movement or Plus Directional Movement (+DM) or absolute down movement or Minus Directional Movement (-DM) is determined.

If the price has moved up, the distance between present high and previous high is taken as +DM. Similarly, if the price has moved down, the distance between the present low and previous low is taken as -DM.

Here please note that “+” and “-” denotes only upward and downward movement. “-DM” is not a negative number. But a positive number of a downward movement.

In case of an outside day, the greater movement is considered and the smaller movement is neglected. That is if the +DM is greater then the -DM is neglected and if the -DM is greater then the +DM is neglected.

In case of an inside day or a same price range day, no recording is done because there is no up or down price movement compared to the previous time period.

Then Directional Index is calculated by dividing Directional Movement by True Range.

That is, Directional Indicator of day 1 = Directional Movement of day 1 / True Range of day 1

+DI1 = (+DM1 / TR1) X 100
and
-DI1 = (-DM1 / TR1) X 100

Like this DI is calculated for 14 days. On 14th day the formula will be:

+DI14 = (+DM14 / TR14) X 100
and
-DI14 = (-DM14 / TR14) X 100

Later on 14 days average of +DM, -DM and TR is first calculated as follows.

First simple average is calculated by adding the values of +DM, -DM and TR for 14 days and dividing it by 14.

On 15th day, 13 parts of previous 14 day average values of +DM, -DM and TR is taken. To that latest day values are added.

So after 15 days the formula for the latest 14 day average of +DM, -DM and TR is:

Latest +DM14 = [Previous +DM14 - (Previous +DM14 / 14)] + Latest +DM1

Latest -DM14 = [Previous -DM14 - (Previous -DM14 / 14)] + Latest -DM1

and

Latest TR14 = [Previous TR14 - (Previous TR14 / 14)] + Latest TR1

With this formula to find the average, more weight is given to the latest value.

Using these values, useable Directional Index or DI is calculated using the formula:

Latest +DI = (Latest +DM14 / Latest TR14) X 100
and
Latest -DI = (Latest -DM14 / Latest TR14) X 100

This 14 days Directional Index or DI is used in the graphs for analysis. Both +DI and -DI are positive numbers. When the trend is going up the +DI keeps increasing and -DI keeps decreasing. When the trend is going down the +DI keeps decreasing and -DI keeps increasing.

When an uptrend changes to down trend -DI crosses above +DI and When the downtrend changes to up trend +DI crosses above -DI.

So a long trade is taken when +DI crosses above -DI and a short trade is taken when -DI crosses above +DI.

More wider they are, stronger the trend. More narrower they are, weaker the trend.

Both Plus Directional Indicator (+DI) and Minus Directional Indicator (-DI) are used to calculate ADX or Average Directional Movement Index, which indicates the strength of the trend. Do not make trading decisions based on any one indicator alone. Any indicator works better when the instrument is moving in an up trend or in a down trend.

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