Profit by DMI and ADX
By Lebo and Lucas:
Directional Movement Indicator (DMI)
Average Directional Movement Index (ADX)
The vast majority of profitable trading systems involve some form of trend following, however most of the time they are not in a trend strong enough to produce worthwhile returns. For the reason that successful traders employ the tactic of taking small losses and letting the profits flow, non-trend markets seem to generate only small losses. As a result, those who follow the trend tend to lose money and most of the time in most markets. Their cherished dream of success is due to finding a random market with a trend strong enough to bring in big profits. A common method of "finding" big trends is to invest in different markets in the hope of hitting one of the profitable markets. Unfortunately, such investing adds more losing markets than winning ones. The usual procedure for investing consists of seeking the best market results by hitting a few good markets while having to endure a wide range of bad ones.
Fortunately, there is a very practical solution to the problem of identifying and measuring the trend direction of the market. A proper interpretation of the Average Directional Movement Index (ADX) allows traders to significantly improve their performance in finding good markets and cutting off the bad ones. We have probably done more research and work with the ADX than any other indicator because we have found the ADX to be an amazingly valuable technical tool with many practical applications. In order to give our readers a complete understanding of the ADX, we must begin with a basic explanation of the Directional Movement Indicator (DMI) used to derive the ADX.
The DMI Concept
Directional Movement is a concept that J. Wells Wilder Jr. first described in his 1978 book "New Concepts in Technical Trading System", a classic work on technical analysis that we heartily recommend. (See "Recommended Reading" at the end of the chapter.) The Directional Movement Indicator (DMI) is a useful and versatile technical study that has two remarkable functions. First, the DMI itself is an excellent market directional indicator. Second, one derivative of the DMI is the important Average Directional Movement Index (ADX), which not only allows us to identify markets that are trending, but also provides a way to assess trend strength.
The calculation of directional movement (DI) is based on the assumption that when there is an uptrend, today's price peak should be higher than yesterday's. Conversely, when there is a downtrend, today's bottom price should be lower than yesterday's. The difference between today's and yesterday's peak is an upward move or +DI. The difference between today's and yesterday's troughs is a downward move or -DI. Internal days where today's peak or trough is not superior to yesterday's are essentially ignored. The positive and negative DI are separately averaged over a period of a few days and then divided by the average "true range". The results are normalised (multiplied by 100) and shown as oscillators. For readers with mathematical inclinations, we have included detailed calculations. Fortunately, we can now produce the necessary indicators with only three or four taps on the computer keyboard.
Calculation of Directional Movement (DM - Directional Movement)
1.A Directional Movement is the largest part of today's price range that is outside yesterday's range.
2. Outside days will have both +DM and -DM. Use the larger one.
3. The inside days have zero DM.
4. Limit days will have a DM calculated as in the diagrams shown above. For example, for an upper limit day (first chart) +DM will be the difference between A and the upper limit reached on the next C day.
1. Measure the directional movement (DM).
2) Measure the true range (TR - true range) which is defined as the greater of:
a) The distance between today's peak and today's trough.
b) The distance between today's peak and yesterday's close.
c) The distance between today's trough and yesterday's close.
Divide DM by TR to obtain a directional indicator
(DI- directional indicator).
The result can be positive or negative. If it is positive, it is the percentage of the true range that has risen on the day. If it is negative, it is the percentage of true range that is down for the day. +DI and -DI are usually averaged over a time period. Wilder recommends 14 days. Then we get the following calculations:
+DI14 = +DM14/TR14 or -DI14 = -DM14/TR14
+DI and -DI are two of the three values normally shown as DMI. The third is the ADX obtained as follows:
4. Calculate the difference between +DI and -DI. DI DIFF=|[(+DI)-(-DI)]|
5. Calculate the sum of +DI and -DI.
6. Calculate the directional index of motion (DX).
DX=( DI DIFF/ DISUM)*100
100 normalises the value of DX so that it falls between 0 and 100. The DX itself is usually very volatile and is not shown.
7. Calculate the moving average DX to obtain the Average Directional Movement Index (ADX). The smoothing is usually on the same number of days as the +DI and -DI calculation.
8. Further smoothing can be done by calculating a derivative of the ADX moment type called the average directional movement index rating (ADXR -average directional movement index rating).
ADXR = (ADX t + ADX t-n) /2
where t is today and t-n is the day the ADX calculation started.
Displayed on the computer screen as an oscillator, directional movement moves upwards when +DI is greater than -DI. If +DI is less than -DI, the movement is directed downwards. As the two lines diverge, the directional movement increases. The greater the difference between +DI and -DI, the greater the directionality of the market or the steeper the trend. Wilder used 14 days as the basis of his calculations because he considered 14 days an important half cycle. We think there are more optimal time periods depending on what you are going to do with DMI and ADX.
DMI studies on a computer monitor usually appear as three lines: +DI, -DI and ADX. (Some programs present the ADX separately for convenience.) As we said, the results of DMI calculations are normalized (multiplied by 100), so the lines will fluctuate between 0 and 100. The important ADX indicator is derived directly from +DI and -DI and measures the magnitude of the market trend. The higher the ADX, the more directional the market has moved. Correspondingly, the lower the ADX, the less directional the market has moved. Note that when we say "directional" we can mean either upward or downward. The ADX does not distinguish between a rising and falling market. It is important to clearly understand that the ADX measures the magnitude of a trend, not its direction. It is perfectly normal for the ADX to clearly rise while prices are falling because its rise reflects the increasing strength of the downtrend.
The other oscillators, +DI and -DI, show the direction. When +DI crosses with -DI and goes higher, the trend is up. When +DI crosses with -DI and goes lower, the trend is downward. The further apart the lines then diverge, the stronger the trend. (See Figure 2-1).
In his book, Wilder also describes the calculation of the average directional moving index rating or ADXR (average directional moving index rating). This is simply the sum of the ADX at the beginning of the period (say 14 days ago) and today's ADX divided by two. This extra smoothing of the ADX was done by Wilder to attenuate the fluctuations to the point where ADXR can be used in a market comparison calculation called the Commodity Selection Index. From our perspective, the ADX
has been sufficiently smoothed initially and additional smoothing is not necessary. In fact, for our purposes, the smoothing that has been done to produce the ADXR reduces the performance of the indicator.
DMI Performance Testing
Quite a few DMI and ADX performance tests have been published. The results have generally been better than most other indicators. Here we will give some examples.
Bruce Babcock has tested the DMI and described the results in his book "The Dow Jones - Irwin Guide to Trading Systems" (see references at the end of the chapter). When testing the DMI, Babcock entered into a long position at the close when the general directional movement was positive. When the general directional movement was negative, the system conversely entered into a short position. The results of Babcock's testing showed that over a five-year period, the 28-day DMI was profitable over a wide range of markets. However, the internal losses were significant because no stops were applied. The system tested by Babcock was the simplest use of the indicator and many of Wilder's basic rules were broken. Importantly, Wilder's suggestion to use waiting for the top or bottom of the day to cross the DI on entry was ignored (we found Wilder's recommendation for entry significantly reduces twitching). In Babcock's test, income was taken clearly at the crossovers and no attempt was made to take income earlier. The fact that the DMI showed significant returns under these conditions is amazing! Although we do not recommend trading DMI in this way, the Babcock test showed that a fairly long DMI could prove to be a useful indicator for setting entry times.
A more realistic test/optimisation was conducted by Frank Hochheimer of Merill Lynch Commodities. Hochheimer tested two cases: case 1, which followed Wilder's basic rules, and case 2, which simply traded on crossovers. Most of the markets used 11 years of data. Since this test was also optimization, it tested +DI and -DI by independently changing the number of days used in each (something we don't recommend doing). Not surprisingly, case 1, which followed Wilder's suggestion of entering a buy or sell at the level of the previous day's peak or trough, proved more profitable. Optimisation of DI periods showed that the best time intervals lay between 14 and 20 days. Our independent testing of ADX on different data sets confirms the profitability of this range from 14 to 20 days with the best results shown on 18 days.
The Encyclopedia of Technical Market Indicators, Colby and Meyers did a very curious DMI test with the ADX built in. They entered at the +DI and -DI intersection only when the ADX was rising. They exited when the ADX fell or a reverse crossover occurred. They only tested the New York Composite on weekly data, using intervals from 1 to 50. The best returns were on time intervals of 11 to 20 weeks. They noted that of the many indicators they tested, the DMI method had the fewest losses and is worth further investigation.
At first glance it may appear that Colby and Mairs were following the trend, trading only on the rise of the ADX. However, because they applied trading based on +DI and -DI crossovers after the ADX rise, the system was more of a counter-trend method because the rising ADX was the result of the presence of the trend before the current crossover. When +DI and -DI crossed after the ADX rose, it was a signal to trade in the opposite direction of the trend as measured by the rising ADX.
We find the ADX moderately useful as a timing indicator, despite some positive test/optimisation results mentioned earlier. The DMI is a trend following indicator, and is subject to the same weaknesses as any form of trend following. When markets are not in trend, +DI and -DI cross in different directions constantly, producing one painful twitch after another. These are sensitive indicators that give good results in trend-following markets, but it is precisely this sensitivity that leads to twitching when the market gets into a sideways trend. However, we are very enthusiastic about using the ADX as a derivative of the DMI as a filter to help select the most successful trading method for each market at any time.
We suspect that the ADX indicator is often neglected due to the obvious drawback of its lack of correlation with price movements. Someone examining the ADX rising in passing while prices are falling could conclude that the indicator gives false signals about the direction of the market. It is critical to properly understand from the start that the ADX alone does not tell you the direction of the market. The ADX can fall when prices are rising and rise when they are falling. The purpose of the ADX is to measure the strength of a trend, not its direction. To determine the direction of the market, you must use additional indicators such as DMI. (See Figure 2-2.)
Some technical analysts attach great importance to the ADX level as an indicator of trend strength, and they would argue that a value of 28 indicates a stronger trend than a value of 20. We have found that the direction of the ADX is much more indicative than its absolute value. A change upwards, for example from 18 to 20,
shows a stronger trend than a negative change from 30 to 28. A good basic rule of thumb could be formulated as follows: as long as the ADX is rising, any ADX value above 15 indicates a trend. We recommend you become familiar with ADX and use it in conjunction with your favourite technical indicators. You will soon discover certain levels of rising ADX produce outstanding results with your favourite indicator. One indicator works well when the ADX rises above 15, and another works well when the ADX rises above 25. When the ADX begins to decline at either level, it is an indication that the market has gone sideways and is forming a sideways trend. We'll explore the significance of rising and falling ADX in more detail and suggest suitable trading strategies. (See Figure 2-3.)
A rising ADX indicates an advancing strong trend and suggests the incorporation of trend-following trading strategies. Technical indicators that need strong trends, such as moving average crossovers and breakout methods, to generate large returns should work very well. Almost any trend following method should produce excellent results in a favourable environment, predicted by a rising ADX. (See Figure 2-4.)
Keep in mind that a rising ADX also provides valuable information about which trading technique might fail. Knowing what not to do can be just as important as knowing what to do. For example, popular trading techniques use overbought/oversold oscillators, such as RSI or stochastic oscillator, and look for sell signals when the market is trading at overbought levels. However, if the ADX is rising steadily, it should serve as a warning that a strong uptrend is underway and the oscillators' sell signals should be ignored. When the ADX is rising, overbought/oversold indicators tend to approach one extreme or the other and remain at that level, giving repeated signals to trade against the trend. If you follow the oscillator signals, the losses can become very significant. The fact that the ADX is rising does not necessarily mean that we cannot use our favourite oscillators. It simply means that we must accept signals going in the direction of the trend. (See Figures 2-5 and 2-6.)
A falling ADX
Falling ADX indicates a non-trending market, where we should use a counter-trend strategy instead of trend following techniques. Overbought or oversold oscillators, which give signals to buy on troughs and to sell on rises, are the preferred strategies when the market is in such a trading corridor. Indicators such as the stochastic oscillator and RSI should give correct signals when the price is fluctuating within the limited area of its trading range.
Due to the fact that buying on troughs and selling on uptrends produces very modest returns at best, many traders prefer to trade only in the direction of the major trends. In that case, it would be best to simply ignore trend-following signals while the ADX is falling. Of course, ideally one would like to have a profitable counter-trend strategy in addition to a trend following strategy, and apply each method in line with the direction of the ADX. (See Figure 2-7.)
ADX Problems: Spikes
We would be doing a bearish disservice by claiming that ADX will solve every problem a trader can encounter. ADX also has its own disadvantages. One problem is that on long periods (we prefer 18 days, as mentioned earlier), which are best applied to most markets, the ADX suddenly changes direction, taking the form of a spike. Spikes usually occur at market peaks when prices suddenly shift from a strong uptrend to a strong downtrend. The source of the problem with the ADX is that it cannot correctly recognise a new downtrend. ADX will still include in its calculations a historical period with a strong move in the positive direction, while at the same time taking data from a new period with a strong move in the negative direction. As a result of the input conflict, the ADX will fall for a while until the old movement in the positive direction is squeezed out of the data, at which point the ADX will begin to rise again due to the new downtrend. In a market that has produced a spike, the ADX may not alert to the trend in time, preventing it from catching much of the rapid downtrend. (See Figure 2-8.)
We will try to find a solution to this problem. One possibility is to switch to a shorter ADX period when the market is at a level where a spike can be expected. We have noticed that some markets often produce spikes (such as metals and grains), while others tend to produce flat tops (Treasuries and securities). ADX does very well on flat tops without the kind of problems that arise on spikes. We would prefer to refrain from any subjective classification of markets, if at all possible, so we continue our search for more objective solutions. Fortunately, market troughs rarely take the form of spikes and the ADX does a very timely job of identifying uptrends as they develop.
ADX problems: Lagging
One characteristic of the ADX that can turn into a problem is that it is slightly slower than many other technical studies. When the ADX begins to rise, many trend-following indicators will already give a signal to enter. For example, +DI and -DI will cross before the ADX begins to rise. It is more than likely that at the time of this early entry signal, the ADX was still falling, so the entry will need to be ignored. In practice, in this situation, the rising ADX becomes a signal of timing to enter the market in the direction of the trend. Faster technical studies are able to determine the direction of the trend, and the ADX is used to set the time of entry. During a trend, faster indicators can provide additional entry signals which, if the ADX continues to rise, must be followed. You will find that some thought and planning will be required to coordinate the ADX with other technical tools.
We view the delay as a small price to pay in order to avoid the costly twitching that can occur if you enter a trade during an ADX deviation. However, the lag time can be set depending on market characteristics and individual trader's preferences. A few markets are more likely to be in a trend than others. For example, the currency markets have moved well over the last few years. In markets which have been trending well, the time frame of the ADX could be shortened to produce faster signals. If lagged entries are frustrating for you, shorten the ADX time frame. If twitching frustrates you, keep the ADX period at 18 days. Lagging is not a problem when using a counter-trend strategy during an ADX drop.
Day Trading with ADX
Perhaps due to distortions caused by large gaps between yesterday's close and today's open, ADX does not work as well when applied to charts with a period of less than one day. Using a 5-minute chart and ADX with a period of 12, the gaps between the open and close can be wiped out after an hour of trading, and the ADX will give the usual first hour trend strength information. However, many day traders prefer to use 20-minute or 15-minute charts, in which case it is difficult to avoid possible DMI and ADX distortions caused by gaps between the close and the open.
More often than not, the standard 18-day ADX can provide valuable long-term information which helps in day trading. The day trader should pay attention to the presence of any trend indicated by a rising ADX, and only enter short-term trades if they are going in the same direction as the trend. When the ADX is falling, short-term trades can be held in either direction. Almost any day trading method can be improved by first checking the ADX to determine if a trend exists. (See Figure 2-9.)
In short, we consider the ADX to be one of the most useful technical indicators. When we trade our management programmes, we usually look at the ADX first before performing further analysis. We find that the trend measure extracted from the ADX is an invaluable guide in choosing the best strategy for each market. The simple but important information provided by the ADX allows us to increase our winning percentage in trades by a significant amount. Many of our trend-following results tests only show the importance and value of the ADX when it rises. Waiting for the ADX to rise often means a delay in relation to our desired entry time, but the belief in mandatory trading success combined with the obvious benefits of reducing the number of losing trades is a more important reward.
In addition to its usefulness on entries, the ADX can be an exceptional help in timing exits from trades. An important pattern noted by Wilder is the possible short-term top or bottom, heralded by the intersection of the +DI, -DI and ADX lines. A market turning point often occurs when the ADX line first turns down, after the ADX crosses first +DI and then -DI from below. We agree with Wilder's conclusion that this downward pivot could be a good time to lock in gains following the trend, or at least close most contracts that are part of a profitable multi-contract position. (See Figure 2-10.)
The ADX can be very useful to exit in a different way. When the ADX is falling, it shows that we should take a small income instead of letting the income flow in. When the ADX is rising, it shows the possibility of large returns and therefore we should refrain from exiting prematurely. Having an accurate indication of when to take small profits and when to expect large returns can be a huge advantage to any trader. This rarely mentioned use of ADX can be just as important as its use in choosing an entry technique.