Volatility and ADX PDF

### [VOLATILITY AND THE DIRECTIONAL MOVEMENT SYSTEM ] ### ### [Volatility] ### One of the key problems faced by all traders is that whether the security they have chosen to be involved with will experience trading or trading range characteristics. The distinction is very important. A trading ran...

### [VOLATILITY AND THE DIRECTIONAL MOVEMENT SYSTEM ] ### ### [Volatility] ### One of the key problems faced by all traders is that whether the security they have chosen to be involved with will experience trading or trading range characteristics. The distinction is very important. A trading range market would be attacked by selling into an overbought reading and buying into an oversold one. Short positions would be initiated with an overbought condition and covered with an oversold one. On the other hand if it is known ahead of time that a market is likely to trend, greater emphasis can be placed on to the trend following devices such as moving averages and trend lines with less significance oscillators. ### ### After all if you believe that a market will continue to rally, why make trading decisions based on a momentum indicator that is likely to undergo several negative divergences with the price before the final peak. ### ### The directional movement system measures each security on a scale of 0 to 100. Those with likely trading range characteristics are ranked at the lower end of the range and those with trading range characteristic at the higher end. Knowing where a specific security may fall enables you to decide intelligently whether to trade the stock from a trending or trading range perceptive. Any securities that fall into either extreme offers good opportunities for low risk profits because trading tactics can be adapted to suit the indicated characteristics. Those securities that fall in the middle would be ignored. Since all securities alternate between trading and trending range characteristics, the system is dynamic because it monitors these characteristics on a continual basis. ### ### [True Range ] Price movements are best measured in proportions rather than arithmetic numbers. This enables us to make a more realistic comparison between two periods or two securities of differing price magnitude. For e.g. A +DM measurement of \$1 for IBM stock trading at \$100 would have a very different implication than a \$1 move for an issue worth \$2 since the former would represent a 1% move and the latter a 50% one. Wilder deals with this problem by comparing +DM and --DM and he calls it the true range. He defines this as the maximum range that the price has moved either during one days trading or from the close of the previous day's trading to the extreme point the following day. This means in effect, that the true range in price is the greatest of the following. The distance between Today's high and today's low. The distance between Yesterday's close and today's high. The distance between Yesterday's close and today's low. The directional indicator (DI) is calculated by dividing the directional movement by the true range. The formula for one day is. **+ DI*1 = (+ DM1 / TR1) and -DI1 = (- DM1 / TR1)*** *TR1* reflects the true range for today and the DM1 the directional movement for day one. The +DI1 formula would be used for the up days and the --DM1 for the down days, since directional movement can occur only in one direction during one day. It is also important to note that directional movement can only be positive. This means that the --DM refers only to down day not the negative number. One day does not make a trend, so it is normal practice to calculate the formula over a number of days. Wilder recommended 14 days since that represents 28-day lunar cycle. This formula reads as follows. **+DI14 = (+DM14 / TR14) and -DI14 = (- DM14 / TR14)** Here the DM14 is the sum total of 14 days of directional movement and TR14 the sum total of 14 days of true ranges. The accumulation method gives us the formula for day 15. That method works like this: Take yesterday's +DM14, divide it by 14 and subtract this quotient from yesterday's +DM14 for today. Calculating the TR14 is done in the same manner. Of course there is no reason why other time spans such as 30 days or 10 days periods cannot be used or even other forms of data such as weekly, monthly etc. The advantage of using this method of calculation is that it does not require us to process and maintain 14 days worth of back data once we have made the first DI14 calculation. A second benefit is that it gives the final indicators a smoothing effect. The actual formulas are given below. **+DM14 (today) = Previous +DM14 - ((Previous +DM14) /14) + DM1** **and** **-DM14 (today) = Previous --DM14 - ((Previous --DM14) / 14)+ -DM14** These two formulas are each divided by the TR14 and multiply the results by 100 to get the plus and minus directional indicators. If the answer to the +DM formula, for e.g. is 15% and the --DI13 is 25% this means 15% of true range prices over the last 14 days was directional and the balance of 60% was non-directional. The figure we are looking for though is the difference between +DI14 and --DI14 because that figure reflects the true direction of the price movement. For instance, if the +DI14 and the --DI14 are identical it would mean that up days more or less offset the down days. In other words, there was no directional movement at all. Using the same logic, if the direction is up for 10 to12 days the +DI would have a high value and the --DM would be very low, resulting in a very high directional movement. All these calculation result in the indicator called the directional movement index (DX) that measures the difference between the two DI's. The DX is calculated by dividing the difference between +DI14 and --DI14 by the sum of the DI14 and the --DI14. The sum reflects the total of the percentage of days that experienced directional movement. The difference is the net result of the type of movement, either plus or minus. By the very nature of calculation the DX will always fall between 0 and 100. The higher the number, greater is the directional movement. The direction of the price movement has no bearing on the DX itself since the DX indicates only the trending characteristics. Lets examine the DX further to see how it works. If the price moves down sharply and then stabilizes, the DX will move from a high number as it did between point B and C in the figure. Then, as the price continues to rally or starts to decline again, as it did in the example, the DX rallies once again. The low DX numbers between points C and D indicates low directional movement. Only after prices resume their decline does the DX rally once more. This low reading between C and D is because the difference between +DX14 and --DX14 is decreasing, occasionally touching 0. The time span used in construction of DX has important implications for directional movements in the same way that changes in the time span of moving average, ROC or Stochastic do. If the standard time span of 14 days is used, the assumption is that the 28 days lunar cycle is the predominant one for short-term trends. However, all cycles can and do fail to operate because the price trends are determined by the interaction of many different cycles, each of which has a varying influence on the trend. Thus if other cycles in a combination has a larger than normal influence because of the way in which they are combined, it will mean that the 2 day cycle will fail to have its normal strong influence. Consequently indicators constructed to reflect this cycle will not have their usual reliable characteristics. Wilder recommends smoothing out the action of the DX in order to make it indicative of the price movements of both the high and low extremes. To do this he suggests calculating DX using a period twice as long as one used for calculating the DI14. A short cut is to take a 14 days average of DX. This average is known as the average directional movement index (ADX). **[Average Directional Movement Index Rating ]** Another feature of the directional movement system is the calculation of the average directional movement index rating. (ADXR) The ADXR is the indicator used to rate the directional characteristics of all the securities we might want to trade. The formula for ADXR is as follows. **ADXR = ((ADXR today+ ADX 14 days ago) / 2** We have used 14 days Wilder recommended as default. It is possible of course to substitute any time period one prefers. According to Wilder the first step is to identify those securities which have a high directional movement, and then to determine when that directional movement is likely to develop. The ratio is developed by dividing the number 2 with ADXR today plus(+) the ADX 14 days ago. When the ADX and the ADXR are plotted together, the ADXR has the appearance of a moving average running through and indicator (the ADX) that is fluctuating around it, or a sort of sine curves as in the **figure.** The chart shows the peak and through, that the ADX measures directional changes only and not the direction of the change. Thus in a bull market a peak indicates a reversal to the downside, but in a bear market it reflects a change from down to up. The larger the difference between the highs and lows in the ADX the greater the reactions resulting in greater trending characteristics. In general it is usually wiser to trade only in the direction of the main trend, but if the amplitude of the movements in the ADX are substantial it means that profitable trend following trades could be made in either direction. The ADXR according to Wilder is exclusively a rating device and should only be used as measurement of directional movement. The greater the distance between the ADXR and zero the greater the directional movement of the security being monitored. **[Plus and Minus DI Crossovers ]** The equilibrium point is when +DI14 and --DI14 are the same level. Buy and sell signals are generated when +DI13 and --DI14 cross. This means that good trade able directional movement, but also movement in excess of the equilibrium point. **[Interpretation]** Wilder believes that the first step in interpreting the directional movement system is to select a security with a high ADX and ADXR reading. This provides sufficient directional movement to make tradable profits from trend following signals. Buy signals in an up market are generated when the +DI14 crosses above the --DI14 and sell signals when +DI14 moves below the \_DI14. In a declining market negative crossovers would be used to take short positions that substantially would be covered when the +DI14 crosses back above the --DI14. In short ADX is used t identify securities that are likely to trend, and the D's are used for actual timing purposes, just as we might use a moving average crossover, trend-line violation or price pattern completion. There is one more feature of the directional movement system called the "extreme rule" This rule state that on the day that DI's cross, use the extreme price that security reached that day as the reversal point. Long positions would use the low price of the day for the purpose of calculation.