### What is the Directional Movement Index (DMI)?

The Directional Movement Index, or DMI, is an indicator developed by J. Welles Wilder in 1978 that identifies in which direction the price of an asset is moving. The indicator does this by comparing prior highs and lows and drawing two lines: a positive directional movement line (+DI) and a negative directional movement line (-DI). An optional third line, called directional movement (DX) shows the difference between the lines. When +DI is above -DI, there is more upward pressure than downward pressure in the price. If -DI is above +DI, then there is more downward pressure in the price. This indicator may help traders assess the trend direction. Crossovers between the lines are also sometimes used as trade signals to buy or sell.

### Key Takeaways

• The Directional Movement Index (DMI) is composed of two lines, and an optional one, showing selling pressure (-DI), showing buying pressure (+DI), and a third DX line showing the difference between the former positive and negative lines.
• A +DI line above the -DI line means there is more upward movement than downward movement.
• A -DI line above the +DI line means there is more downward movement than upward movement.
• Crossovers can be used to signal emerging trends. For example, the +DI crossing above the -DI may signal the start of an uptrend in price.
• The larger the spread between the two lines, the stronger the price trend. If +DI is way above -DI the price trend is strongly up. If -DI is way above +DI then the price trend is strongly down.
• The Average Directional Movement Index (ADX) is another indicator that can be added to the DMI.

### The Formulas For the Directional Movement Index (DMI) are

﻿\begin{aligned} &\text{+DI} = \left ( \frac{ \text{Smoothed +DM} }{ \text{ATR } } \right ) \times 100 \\ &\text{-DI} = \left ( \frac{ \text{Smoothed -DM} }{ \text{ATR } } \right ) \times 100 \\ &\text{DX} = \left ( \frac{ \mid \text{+DI} - \text{-DI} \mid }{ \mid \text{+DI} + \text{-DI} \mid } \right ) \times 100 \\ &\textbf{where:}\\ &\text{+DM (Directional Movement)} = \text{Current High} - \text{PH} \\ &\text{PH} = \text{Previous high} \\ &\text{-DM} = \text{Previous Low} - \text{Current Low} \\ &\text{Smoothed +/-DM} = \textstyle{ \sum_{t=1}^{14} \text{DM} - \left ( \frac{ \sum_{t=1}^{14} \text{DM} }{ 14 } \right ) + \text{CDM} } \\ &\text{CDM} = \text{Current DM} \\ &\text{ATR} = \text{Average True Range} \\ \end{aligned}﻿

### Calculating the Directional Movement Index (DMI)

1. Calculate +DM, -DM, and True Range (TR) for each period. Typically 14 periods are used.
2. +DM is the Current High - Previous High.
3. -DM is the Previous Low - Current Low.
4. Use +DM when Current High - Previous High is greater than Previous Low - Current Low. Use -DM when Previous Low - Current Low is greater than Current High - Previous High.
5. TR is the greater of the Current High - Current Low, Current High - Previous Close, or Current Low - Previous Close.
6. Smooth the 14-period averages of +DM, -DM, and TR. Below is the formula for TR. Insert the -DM and +DM values to calculate the smoothed averages of those as well.
7. First 14TR = Sum of first 14 TR readings.
8. Next 14TR value = First 14TR - (Prior 14TR/14) + Current TR
9. Next, divide the smoothed +DM value by the smoothed TR value to get +DI. Multiply by 100.
10. Divide the smoothed -DM value by the smoothed TR value to get-DI. Multiply by 100.
11. The optional Directional Movement Index (DX) is +DI minus -DI, divided by the sum of +DI and -DI (all absolute values). Multiply by 100.

The Average Directional Movement Index, or ADX, is a smoothed average of DX.

### What Does the Directional Movement Index (DMI) Tell You

The DMI is primarily used to help asses trend direction and provide trade signals.

Crossovers are the main trade signals. A long trade is taken when the +DI crosses above -DI and uptrend could be underway. A sell signal occurs when the -DI drops below -DI. A short trade is initiated when -DI drops below +DI because a downtrend could be underway.

While this method may produce some good signals, it will also produce some bad ones since a trend may not necessarily develop after entry.

The indicator can also be used as a trend or trade confirmation tool. If the +DI is well above -DI, the trend has strength to the upside and this would help confirm current long trades or new long trade signals based on other entry methods. If -DI is well above +DI this confirms the strong downtrend or short positions.

### The Difference Between the Directional Movement Index (DMI) and the Aroon Indicator

The DMI indicator is composed of two lines, with an optional third line. The Aroon Indicator also has two lines. The two indicators both show positive and negative movement, helping to identify trend direction. The calculations are different though, so crossovers on each of the indicators will occur at different times.

### Limitations of the Directional Movement Index (DMI)

The directional movement index (DMI) is part of a larger system called the Average Directional Movement Index (ADX). The trend direction of DMI can be incorporated with the strength readings of the ADX. Readings above 20 on the ADX means the price is trending strongly. Whether using ADX or not, the indicator is still prone to producing lots of false signals.

+DI and -DI readings and crossovers are based on historical prices and don't necessarily reflect what will happen in the future. A crossover can occur, but the price may not respond, resulting in a losing trade. The lines may also crisscross, resulting in multiple signals but no trend in the price. This can be somewhat avoided by only taking trades in the larger trend direction based on long-term price charts, or incorporating ADX readings to help isolate strong trends.