The DMI, Directional Movement Index, is a trend following system. The average directional movement index, or ADX, determines the market trend. When used with the up and down directional indicator values, +DI and -DI, the DMI is an exact trading system.
The rules for using the DMI are simple. You establish a long position whenever the +DI crosses above the -DI. You reverse that position, liquidate the long position and establish a short position, when the -DI crosses above the +DI.
In addition to the crossover rules, you must also follow the extreme point rule. When a crossover occurs, use the extreme price as the reverse point. For a short position, use the high made during the trading interval of the crossover. Conversely, reverse a long position using the low made during the trading interval of the crossover.
You maintain the reverse point, the high or low, as your market entry or exit price even if the +DI and the -DI remain crossed for several trading intervals. This is supposed to keep you from getting whipsawed in the market.
For some traders, the most significant use of the ADX is the turning point concept. First, the ADX must be above both DI lines. When the ADX turns lower, the market often reverses the current trend. The ADX serves as a warning for a market about to change direction. The main exception to this rule is a strong bull market during a blow-off stage. The ADX turns lower only to turn higher a few days later.
According to the developer of the DMI, you should stop using any trend following system when the ADX is below both DI lines. The market is in a choppy sidewise range with no discernible trend.
The computations needed to generate the final figures for the DMI are not complex but are numerous and lengthy. The following discussion attempts to unravel the computational mysteries of the DMI.
If you need further explanation, please refer to the author's original work. The book titled New Concepts in Technical Trading Systems by J. Welles Wilder, Jr. explains this indicator and several others.
You must first compute the directional movement, DM, for the current trading interval. Directional movement can be up, down or zero. If directional movement is up, it is labeled as +DM. The expression -DM refers to downward directional movement.
Wilder defines directional movement as the largest part of the current trading range that is outside the previous trading range. From a mathematical view, it is the largest value of the following differences:
Hight - Hight-1 or Lowt - Lowt-1
This is only true when the current low is less than the previous low, or the current high exceeds the previous high. Please note that both of these conditions do not have to be met, only one. It is the largest portion of the trading range outside of the previous trading range.
It is possible for the directional movement to be zero. This occurs when the current trading range is inside the previous trading range, or the trading ranges, current versus previous, are equal.
Directional movement is up or positive, when the difference between the highs is the greatest. It is down or negative when the difference between the lows is the largest value. Thus, the up directional movement is +DM, and down directional movement is -DM.
Do not let the plus and minus sign designation mislead you. They only indicate upward or downward movement, not values. The directional movement value is always a positive number or absolute value, regardless of upward or downward movement.
This concept is crucial to understanding the computations for the indicator. If you are confused or do not understand, draw some illustrations or work with actual price data to determine the directional movement values.
The next step in determining the DMI is to compute the true range. According to the author, the true range is the largest value of the following equations:
Hight - Lowt
Hight - Closet-1
Lowt - Closet-1
The true range is always a positive number. From this point forward, all references to the true range are designated as TR.
Continue this process for the specified trading interval. In this example, use a value of 14. This is the same value Wilder used on daily data. His logic for using this value is that it represented an average half-cycle period. When this task is accomplished for the specified interval, you compute the average value of the +DM, -DM and TR.
Wilder prefers to use an accumulation technique rather than computing a pure moving average. It was actually a short cut designed to save computational time and effort. That technique is as follows:
Averaget = (Averaget-1 - (Averaget-1 / n)) + Valuet
Thus, when you substitute the above symbols, you have:
+DMt = (+DMt-1 - (+DMt-1 / n)) + (+DMt)
-DMt = (-DMt-1 - (-DMt-1 / n)) + (-DMt)
TRt = (TRt-1 - (TRt-1 / n)) + (TRt)
If you think about it, it really is a timesaving convention. Remember, this indicator was developed before microcomputers were invented. The only tool available was the desktop calculator or adding machine. You could spend a great deal of time and effort calculating averages.
You now have the average values. The next step is to compute the directional indicator. Again, it can either be up or down, depending upon the directional movement. On up intervals, the formula is:
+DI = (+DM / TR) * 100
On a down interval, the formula is:
-DI = (-DM / TR) * 100
The plus and minus directional indicator values are computed as percentage figures. You are expressing the percentage of the average true range for both up and down trading intervals.
If you have followed this process so far, the last few steps are relatively simple. You compute the difference between the +DI and the -DI. Again, you use the absolute value of this difference. Simply, convert any negative value into a positive number. The formula is:
DIdiff = | ((+DI) - (-DI)) |
Next, compute the sum of the directional indicator values. The formula reads as follows:
DIsum = ((+DI) + (-DI))
Once you compute the DIdiff and the DIsum, you calculate the DX or directional movement index. This value is always a percentage. The formula is:
DX = (DIdiff / DIsum) * 100
The DX is always a value between 0 and 100. If your calculations exceed this range, you made an error. Wilder was not comfortable using just the directional movement index. It could become very volatile during periods of extreme price movement, especially markets that rise and fall quickly. Again, he implements his accumulated moving average technique to smooth the DX. The result is the ADX or average directional movement index. The computational procedure is as follows:
ADXt = ( (ADXt-1 * (n - 1) ) + DXt) / n
If the Futures.Quote software appears to be sluggish when you display the DMI study, you know why. The software performs numerous comparisons and calculations to generate the values of the study. Remember, Futures.Quote plots and displays the +DI, -DI, and the ADX values in this order at the top of the page.